diff --git a/main/src/main/scala/sbt/Defaults.scala b/main/src/main/scala/sbt/Defaults.scala
index 056bda08f..be0fb5a42 100755
--- a/main/src/main/scala/sbt/Defaults.scala
+++ b/main/src/main/scala/sbt/Defaults.scala
@@ -47,6 +47,7 @@ import sbt.internal.server.{
   LanguageServerReporter,
   ServerHandler
 }
+import sbt.nio.FileStamp.Formats.seqPathFileStampJsonFormatter
 import sbt.internal.testing.TestLogger
 import sbt.internal.util.Attributed.data
 import sbt.internal.util.Types._
@@ -617,31 +618,42 @@ object Defaults extends BuildCommon {
       s"inc_compile$extra.zip"
     },
     externalHooks := {
-      import sbt.nio.FileStamp.Formats.seqPathFileStampJsonFormatter
+      import sjsonnew.BasicJsonProtocol.mapFormat
       val currentInputs =
         (unmanagedSources / inputFileStamps).value ++ (managedSourcePaths / outputFileStamps).value
-      val previousInputs = (externalHooks / inputFileStamps).previous
+      val sv = scalaVersion.value
+      val previousInputs = compileSourceFileInputs.previous.flatMap(_.get(sv))
       val inputChanges = previousInputs
         .map(sbt.nio.Settings.changedFiles(_, currentInputs))
         .getOrElse(FileChanges.noPrevious(currentInputs.map(_._1)))
       val currentOutputs = (dependencyClasspathFiles / outputFileStamps).value
-      val previousOutputs = (externalHooks / outputFileStamps).previous
+      val previousOutputs = compileBinaryFileInputs.previous.flatMap(_.get(sv))
       val outputChanges = previousOutputs
         .map(sbt.nio.Settings.changedFiles(_, currentOutputs))
         .getOrElse(FileChanges.noPrevious(currentOutputs.map(_._1)))
       ExternalHooks.default.value(inputChanges, outputChanges, fileTreeView.value)
     },
-    externalHooks / inputFileStamps := {
+    compileSourceFileInputs := {
+      import sjsonnew.BasicJsonProtocol.mapFormat
       compile.value // ensures the inputFileStamps previous value is only set if compile succeeds.
-      (unmanagedSources / inputFileStamps).value ++ (managedSourcePaths / outputFileStamps).value
+      val version = scalaVersion.value
+      val versions = crossScalaVersions.value.toSet + version
+      val prev: Map[String, Seq[(java.nio.file.Path, sbt.nio.FileStamp)]] =
+        compileSourceFileInputs.previous.map(_.filterKeys(versions)).getOrElse(Map.empty)
+      prev + (version ->
+        ((unmanagedSources / inputFileStamps).value ++ (managedSourcePaths / outputFileStamps).value))
     },
-    externalHooks / inputFileStamps := (externalHooks / inputFileStamps).triggeredBy(compile).value,
-    externalHooks / outputFileStamps := {
+    compileSourceFileInputs := compileSourceFileInputs.triggeredBy(compile).value,
+    compileBinaryFileInputs := {
+      import sjsonnew.BasicJsonProtocol.mapFormat
       compile.value // ensures the inputFileStamps previous value is only set if compile succeeds.
-      (dependencyClasspathFiles / outputFileStamps).value
+      val version = scalaVersion.value
+      val versions = crossScalaVersions.value.toSet + version
+      val prev: Map[String, Seq[(java.nio.file.Path, sbt.nio.FileStamp)]] =
+        compileBinaryFileInputs.previous.map(_.filterKeys(versions)).getOrElse(Map.empty)
+      prev + (version -> (dependencyClasspathFiles / outputFileStamps).value)
     },
-    externalHooks / outputFileStamps :=
-      (externalHooks / outputFileStamps).triggeredBy(compile).value,
+    compileBinaryFileInputs := compileBinaryFileInputs.triggeredBy(compile).value,
     incOptions := { incOptions.value.withExternalHooks(externalHooks.value) },
     compileIncSetup := compileIncSetupTask.value,
     console := consoleTask.value,
diff --git a/main/src/main/scala/sbt/nio/Keys.scala b/main/src/main/scala/sbt/nio/Keys.scala
index 1f4d85fdf..24983771e 100644
--- a/main/src/main/scala/sbt/nio/Keys.scala
+++ b/main/src/main/scala/sbt/nio/Keys.scala
@@ -168,6 +168,12 @@ object Keys {
   private[sbt] val classpathFiles =
     taskKey[Seq[Path]]("The classpath for a task.").withRank(Invisible)
   private[sbt] val compileOutputs = taskKey[Seq[Path]]("Compilation outputs").withRank(Invisible)
+  private[sbt] val compileSourceFileInputs =
+    taskKey[Map[String, Seq[(Path, FileStamp)]]]("Source file stamps stored by scala version")
+      .withRank(Invisible)
+  private[sbt] val compileBinaryFileInputs =
+    taskKey[Map[String, Seq[(Path, FileStamp)]]]("Source file stamps stored by scala version")
+      .withRank(Invisible)
 
   private[this] val hasCheckedMetaBuildMsg =
     "Indicates whether or not we have called the checkBuildSources task. This is to avoid warning " +
diff --git a/sbt/src/sbt-test/actions/cross-incremental/build.sbt b/sbt/src/sbt-test/actions/cross-incremental/build.sbt
new file mode 100644
index 000000000..39c22fb65
--- /dev/null
+++ b/sbt/src/sbt-test/actions/cross-incremental/build.sbt
@@ -0,0 +1,22 @@
+scalaVersion := "2.12.8"
+crossScalaVersions := List("2.12.8", "2.13.0")
+
+val setLastModified = taskKey[Unit]("Sets the last modified time for classfiles")
+setLastModified := {
+  val versions = crossScalaVersions.value
+  versions.map(_.split('.').take(2).mkString("scala-", ".", "")).foreach { v =>
+    val f = target.value / v / "classes" / "A.class"
+    Stamps.value.put(f, IO.getModifiedTimeOrZero(f))
+  }
+}
+
+val checkLastModified = taskKey[Unit]("Checks the last modified time for classfiles")
+checkLastModified := {
+  val versions = crossScalaVersions.value
+  versions.map(_.split('.').take(2).mkString("scala-", ".", "")).foreach { v =>
+    val classFile = target.value / v / "classes" / "A.class"
+    val actual = IO.getModifiedTimeOrZero(classFile)
+    val previous = Stamps.value.get(classFile)
+    assert(actual == previous, s"$actual did not equal $previous for $classFile")
+  }
+}
diff --git a/sbt/src/sbt-test/actions/cross-incremental/project/src/main/scala/Stamps.scala b/sbt/src/sbt-test/actions/cross-incremental/project/src/main/scala/Stamps.scala
new file mode 100644
index 000000000..e39d1a4fb
--- /dev/null
+++ b/sbt/src/sbt-test/actions/cross-incremental/project/src/main/scala/Stamps.scala
@@ -0,0 +1,3 @@
+object Stamps {
+  val value = new java.util.HashMap[java.io.File, Long]
+}
\ No newline at end of file
diff --git a/sbt/src/sbt-test/actions/cross-incremental/src/main/scala/A.scala b/sbt/src/sbt-test/actions/cross-incremental/src/main/scala/A.scala
new file mode 100644
index 000000000..3c8bfdd75
--- /dev/null
+++ b/sbt/src/sbt-test/actions/cross-incremental/src/main/scala/A.scala
@@ -0,0 +1,3 @@
+object A {
+  def a = 1
+}
\ No newline at end of file
diff --git a/sbt/src/sbt-test/actions/cross-incremental/test b/sbt/src/sbt-test/actions/cross-incremental/test
new file mode 100644
index 000000000..036f3dca0
--- /dev/null
+++ b/sbt/src/sbt-test/actions/cross-incremental/test
@@ -0,0 +1,7 @@
+> +compile
+
+> setLastModified
+
+> +compile
+
+> checkLastModified
diff --git a/scripted-sbt-redux/src/main/scala/sbt/scriptedtest/ScriptedTests.scala b/scripted-sbt-redux/src/main/scala/sbt/scriptedtest/ScriptedTests.scala
index 3afdc0c82..637ebdce6 100644
--- a/scripted-sbt-redux/src/main/scala/sbt/scriptedtest/ScriptedTests.scala
+++ b/scripted-sbt-redux/src/main/scala/sbt/scriptedtest/ScriptedTests.scala
@@ -184,6 +184,7 @@ final class ScriptedTests(
     val (group, name) = testName
     s"$group/$name" match {
       case "actions/add-alias"          => LauncherBased // sbt/Package$
+      case "actions/cross-incremental"  => LauncherBased // tbd
       case "actions/cross-multiproject" => LauncherBased // tbd
       case "actions/cross-multi-parser" =>
         LauncherBased // java.lang.ClassNotFoundException: javax.tools.DiagnosticListener when run with java 11 and an old sbt launcher