diff --git a/R/data.table.R b/R/data.table.R
index 66fa75f50..751e2f3f3 100644
--- a/R/data.table.R
+++ b/R/data.table.R
@@ -2923,9 +2923,8 @@ setDT = function(x, keep.rownames=FALSE, key=NULL, check.names=FALSE) {
       }
     }
 
-    # setalloccol results in a shallow copy. Must be performed before class setting,
-    # to have the class apply only to the new copy. #4784
-    setalloccol(x)
+    # setalloccol results in a shallow copy. Must be performed before class setting not to affect other copies of x (#4784)
+    x = .shallow(x)
 
     rn = if (!identical(keep.rownames, FALSE)) rownames(x) else NULL
     setattr(x, "row.names", .set_row_names(nrow(x)))
@@ -2933,7 +2932,8 @@ setDT = function(x, keep.rownames=FALSE, key=NULL, check.names=FALSE) {
 
     # fix for #1078 and #1128, see .resetclass() for explanation.
     setattr(x, "class", .resetclass(x, 'data.frame'))
-
+    setalloccol(x)
+  
     if (!is.null(rn)) {
       nm = c(if (is.character(keep.rownames)) keep.rownames[1L] else "rn", names(x))
       x[, (nm[1L]) := rn]