diff --git a/NEWS.md b/NEWS.md
index f203117ba..92b4f9ee3 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -107,6 +107,8 @@ rowwiseDT(
 
 11. `tables()` now returns the correct size for data.tables over 2GiB, [#6607](https://github.com/Rdatatable/data.table/issues/6607). Thanks to @vlulla for the report and the PR.
 
+12. Joins on multiple columns, such as `x[y, on=c("x1==y1", "x2==y1")]`, could fail during implicit type coercions if `x1` and `x2` had different but still compatible types, [#6602](https://github.com/Rdatatable/data.table/issues/6602). This was particularly unexpected when columns `x1`, `x2`, and `y1` were all of the same class, e.g. `Date`, but differed in their underlying storage types. Thanks to Benjamin Schwendinger for the report and the fix.
+
 ## NOTES
 
 1. Tests run again when some Suggests packages are missing, [#6411](https://github.com/Rdatatable/data.table/issues/6411). Thanks @aadler for the note and @MichaelChirico for the fix.
diff --git a/R/bmerge.R b/R/bmerge.R
index aa7ea4103..317fe2f64 100644
--- a/R/bmerge.R
+++ b/R/bmerge.R
@@ -1,4 +1,25 @@
 
+
+mergeType = function(x) {
+  ans = typeof(x)
+  if      (ans=="integer") { if (is.factor(x))             ans = "factor"    }
+  else if (ans=="double")  { if (inherits(x, "integer64")) ans = "integer64" }
+  # do not call isReallyReal(x) yet because i) if both types are double we don't need to coerce even if one or both sides
+  # are int-as-double, and ii) to save calling it until we really need it
+  ans
+}
+
+cast_with_atts = function(x, as.f) {
+  ans = as.f(x)
+  if (!is.null(attributes(x))) attributes(ans) = attributes(x)
+  ans
+}
+
+coerce_col = function(dt, col, from_type, to_type, from_name, to_name, verbose_msg=NULL) {
+  if (!is.null(verbose_msg)) catf(verbose_msg, from_type, from_name, to_type, to_name, domain=NULL)
+  set(dt, j=col, value=cast_with_atts(dt[[col]], match.fun(paste0("as.", to_type))))
+}
+
 bmerge = function(i, x, icols, xcols, roll, rollends, nomatch, mult, ops, verbose)
 {
   callersi = i
@@ -25,95 +46,110 @@ bmerge = function(i, x, icols, xcols, roll, rollends, nomatch, mult, ops, verbos
 
   supported = c(ORDERING_TYPES, "factor", "integer64")
 
-  getClass = function(x) {
-    ans = typeof(x)
-    if      (ans=="integer") { if (is.factor(x))             ans = "factor"    }
-    else if (ans=="double")  { if (inherits(x, "integer64")) ans = "integer64" }
-    # do not call isReallyReal(x) yet because i) if both types are double we don't need to coerce even if one or both sides
-    # are int-as-double, and ii) to save calling it until we really need it
-    ans
-  }
-
   if (nrow(i)) for (a in seq_along(icols)) {
     # - check that join columns have compatible types
     # - do type coercions if necessary on just the shallow local copies for the purpose of join
     # - handle factor columns appropriately
     # Note that if i is keyed, if this coerces i's key gets dropped by set()
-    ic = icols[a]
-    xc = xcols[a]
-    xclass = getClass(x[[xc]])
-    iclass = getClass(i[[ic]])
-    xname = paste0("x.", names(x)[xc])
-    iname = paste0("i.", names(i)[ic])
-    if (!xclass %chin% supported) stopf("%s is type %s which is not supported by data.table join", xname, xclass)
-    if (!iclass %chin% supported) stopf("%s is type %s which is not supported by data.table join", iname, iclass)
-    if (xclass=="factor" || iclass=="factor") {
+    icol = icols[a]
+    xcol = xcols[a]
+    x_merge_type = mergeType(x[[xcol]])
+    i_merge_type = mergeType(i[[icol]])
+    xname = paste0("x.", names(x)[xcol])
+    iname = paste0("i.", names(i)[icol])
+    if (!x_merge_type %chin% supported) stopf("%s is type %s which is not supported by data.table join", xname, x_merge_type)
+    if (!i_merge_type %chin% supported) stopf("%s is type %s which is not supported by data.table join", iname, i_merge_type)
+    if (x_merge_type=="factor" || i_merge_type=="factor") {
       if (roll!=0.0 && a==length(icols))
         stopf("Attempting roll join on factor column when joining %s to %s. Only integer, double or character columns may be roll joined.", xname, iname)
-      if (xclass=="factor" && iclass=="factor") {
+      if (x_merge_type=="factor" && i_merge_type=="factor") {
         if (verbose) catf("Matching %s factor levels to %s factor levels.\n", iname, xname)
-        set(i, j=ic, value=chmatch(levels(i[[ic]]), levels(x[[xc]]), nomatch=0L)[i[[ic]]])  # nomatch=0L otherwise a level that is missing would match to NA values
+        set(i, j=icol, value=chmatch(levels(i[[icol]]), levels(x[[xcol]]), nomatch=0L)[i[[icol]]])  # nomatch=0L otherwise a level that is missing would match to NA values
         next
       } else {
-        if (xclass=="character") {
+        if (x_merge_type=="character") {
           if (verbose) catf("Coercing factor column %s to type character to match type of %s.\n", iname, xname)
-          set(i, j=ic, value=val<-as.character(i[[ic]]))
-          set(callersi, j=ic, value=val)  # factor in i joining to character in x will return character and not keep x's factor; e.g. for antaresRead #3581
+          set(i, j=icol, value=val<-as.character(i[[icol]]))
+          set(callersi, j=icol, value=val)  # factor in i joining to character in x will return character and not keep x's factor; e.g. for antaresRead #3581
           next
-        } else if (iclass=="character") {
+        } else if (i_merge_type=="character") {
           if (verbose) catf("Matching character column %s to factor levels in %s.\n", iname, xname)
-          newvalue = chmatch(i[[ic]], levels(x[[xc]]), nomatch=0L)
-          if (anyNA(i[[ic]])) newvalue[is.na(i[[ic]])] = NA_integer_  # NA_character_ should match to NA in factor, #3809
-          set(i, j=ic, value=newvalue)
+          newvalue = chmatch(i[[icol]], levels(x[[xcol]]), nomatch=0L)
+          if (anyNA(i[[icol]])) newvalue[is.na(i[[icol]])] = NA_integer_  # NA_character_ should match to NA in factor, #3809
+          set(i, j=icol, value=newvalue)
           next
         }
       }
-      stopf("Incompatible join types: %s (%s) and %s (%s). Factor columns must join to factor or character columns.", xname, xclass, iname, iclass)
+      stopf("Incompatible join types: %s (%s) and %s (%s). Factor columns must join to factor or character columns.", xname, x_merge_type, iname, i_merge_type)
     }
-    if (xclass == iclass) {
-      if (verbose) catf("%s has same type (%s) as %s. No coercion needed.\n", iname, xclass, xname)
+    # we check factors first to cater for the case when trying to do rolling joins on factors
+    if (x_merge_type == i_merge_type) {
+      if (verbose) catf("%s has same type (%s) as %s. No coercion needed.\n", iname, x_merge_type, xname)
       next
     }
-    if (xclass=="character" || iclass=="character" ||
-        xclass=="logical" || iclass=="logical" ||
-        xclass=="factor" || iclass=="factor") {
-      if (anyNA(i[[ic]]) && allNA(i[[ic]])) {
-        if (verbose) catf("Coercing all-NA %s (%s) to type %s to match type of %s.\n", iname, iclass, xclass, xname)
-        set(i, j=ic, value=match.fun(paste0("as.", xclass))(i[[ic]]))
+    cfl = c("character", "logical", "factor")
+    if (x_merge_type %chin% cfl || i_merge_type %chin% cfl) {
+      msg = if(verbose) gettext("Coercing all-NA %s column %s to type %s to match type of %s.\n") else NULL
+      if (anyNA(i[[icol]]) && allNA(i[[icol]])) {
+        coerce_col(i, icol, i_merge_type, x_merge_type, iname, xname, msg)
         next
       }
-      else if (anyNA(x[[xc]]) && allNA(x[[xc]])) {
-        if (verbose) catf("Coercing all-NA %s (%s) to type %s to match type of %s.\n", xname, xclass, iclass, iname)
-        set(x, j=xc, value=match.fun(paste0("as.", iclass))(x[[xc]]))
+      if (anyNA(x[[xcol]]) && allNA(x[[xcol]])) {
+        coerce_col(x, xcol, x_merge_type, i_merge_type, xname, iname, msg)
         next
       }
-      stopf("Incompatible join types: %s (%s) and %s (%s)", xname, xclass, iname, iclass)
+      stopf("Incompatible join types: %s (%s) and %s (%s)", xname, x_merge_type, iname, i_merge_type)
     }
-    if (xclass=="integer64" || iclass=="integer64") {
+    if (x_merge_type=="integer64" || i_merge_type=="integer64") {
       nm = c(iname, xname)
-      if (xclass=="integer64") { w=i; wc=ic; wclass=iclass; } else { w=x; wc=xc; wclass=xclass; nm=rev(nm) }  # w is which to coerce
+      if (x_merge_type=="integer64") { w=i; wc=icol; wclass=i_merge_type; } else { w=x; wc=xcol; wclass=x_merge_type; nm=rev(nm) }  # w is which to coerce
       if (wclass=="integer" || (wclass=="double" && !isReallyReal(w[[wc]]))) {
         if (verbose) catf("Coercing %s column %s%s to type integer64 to match type of %s.\n", wclass, nm[1L], if (wclass=="double") " (which contains no fractions)" else "", nm[2L])
         set(w, j=wc, value=bit64::as.integer64(w[[wc]]))
       } else stopf("Incompatible join types: %s is type integer64 but %s is type double and contains fractions", nm[2L], nm[1L])
     } else {
       # just integer and double left
-      if (iclass=="double") {
-        if (!isReallyReal(i[[ic]])) {
+      ic_idx = which(icol == icols) # check if on is joined on multiple conditions, #6602
+      if (i_merge_type=="double") {
+        coerce_x = FALSE
+        if (!isReallyReal(i[[icol]])) {
+          coerce_x = TRUE
           # common case of ad hoc user-typed integers missing L postfix joining to correct integer keys
           # we've always coerced to int and returned int, for convenience.
-          if (verbose) catf("Coercing double column %s (which contains no fractions) to type integer to match type of %s.\n", iname, xname)
-          val = as.integer(i[[ic]])
-          if (!is.null(attributes(i[[ic]]))) attributes(val) = attributes(i[[ic]])  # to retain Date for example; 3679
-          set(i, j=ic, value=val)
-          set(callersi, j=ic, value=val)       # change the shallow copy of i up in [.data.table to reflect in the result, too.
-        } else {
-          if (verbose) catf("Coercing integer column %s to type double to match type of %s which contains fractions.\n", xname, iname)
-          set(x, j=xc, value=as.double(x[[xc]]))
+          if (length(ic_idx)>1L) {
+            xc_idx = xcols[ic_idx]
+            for (xb in xc_idx[which(vapply_1c(.shallow(x, xc_idx), mergeType) == "double")]) {
+              if (isReallyReal(x[[xb]])) {
+                coerce_x = FALSE
+                break
+              }
+            }
+          }
+          if (coerce_x) {
+            msg = if (verbose) gettext("Coercing %s column %s (which contains no fractions) to type %s to match type of %s.\n") else NULL
+            coerce_col(i, icol, "double", "integer", iname, xname, msg)
+            set(callersi, j=icol, value=i[[icol]])       # change the shallow copy of i up in [.data.table to reflect in the result, too.
+            if (length(ic_idx)>1L) {
+              xc_idx = xcols[ic_idx]
+              for (xb in xc_idx[which(vapply_1c(.shallow(x, xc_idx), mergeType) == "double")]) {
+                coerce_col(x, xb, "double", "integer", paste0("x.", names(x)[xb]), xname, msg)
+              }
+            }
+          }
+        }
+        if (!coerce_x) {
+          msg = if (verbose) gettext("Coercing %s column %s to type %s to match type of %s which contains fractions.\n") else NULL
+          coerce_col(x, xcol, "integer", "double", xname, iname, msg)
         }
       } else {
-        if (verbose) catf("Coercing integer column %s to type double for join to match type of %s.\n", iname, xname)
-        set(i, j=ic, value=as.double(i[[ic]]))
+        msg = if (verbose) gettext("Coercing %s column %s to type %s for join to match type of %s.\n") else NULL
+        coerce_col(i, icol, "integer", "double", iname, xname, msg)
+        if (length(ic_idx)>1L) {
+          xc_idx = xcols[ic_idx]
+          for (xb in xc_idx[which(vapply_1c(.shallow(x, xc_idx), mergeType) == "integer")]) {
+            coerce_col(x, xb, "integer", "double", paste0("x.", names(x)[xb]), xname, msg)
+          }
+        }
       }
     }
   }
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index fef8f1fff..92db5262c 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -15156,15 +15156,15 @@ if (test_bit64) {
 dt1 = data.table(a=1,  b=NA_character_)
 dt2 = data.table(a=2L, b=NA)
 test(2044.80, dt1[dt2, on="a==b",             verbose=TRUE], data.table(a=NA, b=NA_character_, i.a=2L),
-              output=msg<-"Coercing all-NA i.b (logical) to type double to match type of x.a")
+              output=msg<-"Coercing all-NA logical column i.b to type double to match type of x.a")
 test(2044.81, dt1[dt2, on="a==b", nomatch=0L, verbose=TRUE], data.table(a=logical(), b=character(), i.a=integer()),
               output=msg)
 test(2044.82, dt1[dt2, on="b==b",             verbose=TRUE], data.table(a=1, b=NA, i.a=2L),
-              output=msg<-"Coercing all-NA i.b (logical) to type character to match type of x.b")
+              output=msg<-"Coercing all-NA logical column i.b to type character to match type of x.b")
 test(2044.83, dt1[dt2, on="b==b", nomatch=0L, verbose=TRUE], data.table(a=1, b=NA, i.a=2L),
               output=msg)
 test(2044.84, dt1[dt2, on="b==a",             verbose=TRUE], data.table(a=NA_real_, b=2L, i.b=NA),
-              output=msg<-"Coercing all-NA x.b (character) to type integer to match type of i.a")
+              output=msg<-"Coercing all-NA character column x.b to type integer to match type of i.a")
 test(2044.85, dt1[dt2, on="b==a", nomatch=0L, verbose=TRUE], data.table(a=double(), b=integer(), i.b=logical()),
               output=msg)
 
@@ -15727,7 +15727,8 @@ DT = data.table(z = 1i)
 test(2069.33, DT[DT, on = 'z'], error = "Type 'complex' is not supported for joining/merging")
 
 # forder verbose message when !isReallyReal Date, #1738
-DT = data.table(d=sample(seq(as.Date("2015-01-01"), as.Date("2015-01-05"), by="days"), 20, replace=TRUE))
+date_dbl = as.Date(as.double(seq(as.Date("2015-01-01"), as.Date("2015-01-05"), by="days")), origin="1970-01-01")
+DT = data.table(d=sample(date_dbl, 20, replace=TRUE))
 test(2070.01, typeof(DT$d), "double")
 test(2070.02, DT[, .N, keyby=d, verbose=TRUE], output="Column 1.*date.*8 byte double.*no fractions are present.*4 byte integer.*to save space and time")
 
@@ -20596,3 +20597,33 @@ test(2295.3, is.data.table(d2))
 
 # #6588: .checkTypos used to give arbitrary strings to stopf as the first argument
 test(2296, d2[x %no such operator% 1], error = '%no such operator%')
+
+# fix coercing integer/double for joins on multiple columns, #6602
+x = data.table(a=1L)
+y = data.table(c=1L, d=1)
+test(2297.01, y[x, on=.(c == a, d == a), verbose=TRUE], data.table(c=1L, d=1L), output="Coercing .*a to type double.*Coercing .*c to type double")
+test(2297.02, y[x, on=.(d == a, c == a), verbose=TRUE], data.table(c=1L, d=1L), output="Coercing .*a to type double.*Coercing .*c to type double")
+x = data.table(a=1)
+y = data.table(c=1, d=1L)
+test(2297.03, y[x, on=.(c == a, d == a), verbose=TRUE], data.table(c=1L, d=1L), output="Coercing .*a .*no fractions.* to type integer.*Coercing .*c .*no fractions.* to type integer")
+test(2297.04, y[x, on=.(d == a, c == a), verbose=TRUE], data.table(c=1L, d=1L), output="Coercing .*a .*no fractions.* to type integer.*Coercing .*c .*no fractions.* to type integer")
+# dates
+d_int = .Date(1L)
+d_dbl = .Date(1)
+x = data.table(a=d_int)
+y = data.table(c=d_int, d=d_dbl)
+test(2297.11, y[x, on=.(c == a, d == a)], data.table(c=d_int, d=d_int))
+test(2297.12, y[x, on=.(d == a, c == a)], data.table(c=d_int, d=d_int))
+x = data.table(a=d_dbl)
+y = data.table(c=d_dbl, d=d_int)
+test(2297.13, y[x, on=.(c == a, d == a)], data.table(c=d_int, d=d_int))
+test(2297.14, y[x, on=.(d == a, c == a)], data.table(c=d_int, d=d_int))
+# real double
+x = data.table(a=1)
+y = data.table(c=1.5, d=1L)
+test(2297.21, y[x, on=.(c == a, d == a)], data.table(c=1, d=1))
+test(2297.22, y[x, on=.(d == a, c == a)], data.table(c=1, d=1))
+# non right join
+x = data.table(a=1, b=2L)
+y = data.table(c=1.5, d=1L)
+test(2297.31, y[x, on=.(c == a, d == a), nomatch=NULL], output="Empty data.table (0 rows and 3 cols): c,d,b")