diff --git a/src/main/scala/sbt/VirtualAxis.scala b/src/main/scala/sbt/VirtualAxis.scala
index 2b2648909..7d831682b 100644
--- a/src/main/scala/sbt/VirtualAxis.scala
+++ b/src/main/scala/sbt/VirtualAxis.scala
@@ -23,16 +23,50 @@ object VirtualAxis {
   abstract class StrongAxis extends VirtualAxis
 
 
-  def isMatch(lhs: Seq[VirtualAxis], rhs: Seq[VirtualAxis]): Boolean = {
-    def isCompatible(v: VirtualAxis, stack: Seq[VirtualAxis]): Boolean =
-      v match {
-        case v: WeakAxis =>
-          val clazz = v.getClass
-          stack.contains(v) || !stack.exists(_.getClass == clazz)
-        case v: StrongAxis =>
-          stack.contains(v)
+  def isMatch(lhs: Seq[VirtualAxis], rhs: Seq[VirtualAxis]): Boolean =
+    lhs.forall(isStronglyCompatible(_, rhs)) && rhs.forall(isStronglyCompatible(_, lhs))
+
+  private[sbt] def isStronglyCompatible(v: VirtualAxis, stack: Seq[VirtualAxis]): Boolean =
+    v match {
+      case v: WeakAxis =>
+        val clazz = v.getClass
+        stack.contains(v) || !stack.exists(_.getClass == clazz)
+      case v: StrongAxis =>
+        stack.contains(v)
+    }
+
+  def isSecondaryMatch(lhs: Seq[VirtualAxis], rhs: Seq[VirtualAxis]): Boolean =
+    lhs.forall(isSecondaryCompatible(_, rhs)) && rhs.forall(isSecondaryCompatible(_, lhs))
+
+  def isSecondaryCompatible(v: VirtualAxis, stack: Seq[VirtualAxis]): Boolean =
+    v match {
+      case v: ScalaVersionAxis =>
+        val thatSVOpt = (stack collect {
+          case x: ScalaVersionAxis => x
+        }).headOption
+        thatSVOpt match {
+          case Some(ScalaVersionAxis(sv, _)) =>
+            (v.scalaVersion == sv) ||
+            isScala2Scala3Sandwich(partialVersion(v.scalaVersion), partialVersion(sv))
+          case _ => true
+        }
+      case _ =>
+        isStronglyCompatible(v, stack)
+    }
+
+  private[sbt] def isScala2Scala3Sandwich(sbv1: Option[(Long, Long)], sbv2: Option[(Long, Long)]): Boolean = {
+    def str(x: Option[(Long, Long)]): String =
+      x match {
+        case Some((a, b)) => s"$a.$b"
+        case _            => "0.0"
       }
-    lhs.forall(isCompatible(_, rhs)) && rhs.forall(isCompatible(_, lhs))
+    isScala2Scala3Sandwich(str(sbv1), str(sbv2))
+  }
+
+  private[sbt] def isScala2Scala3Sandwich(sbv1: String, sbv2: String): Boolean = {
+    def compare(a: String, b: String): Boolean =
+      a == "2.13" && (b.startsWith("0.") || b.startsWith("3.0"))
+    compare(sbv1, sbv2) || compare(sbv2, sbv1)
   }
 
   case class ScalaVersionAxis(scalaVersion: String, value: String) extends WeakAxis {
diff --git a/src/main/scala/sbt/internal/ProjectMatrix.scala b/src/main/scala/sbt/internal/ProjectMatrix.scala
index d4e43afc2..50304ddff 100644
--- a/src/main/scala/sbt/internal/ProjectMatrix.scala
+++ b/src/main/scala/sbt/internal/ProjectMatrix.scala
@@ -163,6 +163,9 @@ object ProjectMatrix {
     def isMatch(that: ProjectRow): Boolean =
       VirtualAxis.isMatch(this.axisValues, that.axisValues)
 
+    def isSecondaryMatch(that: ProjectRow): Boolean =
+      VirtualAxis.isSecondaryMatch(this.axisValues, that.axisValues)
+
     override def toString: String = s"ProjectRow($autoScalaLibrary, $axisValues)"
   }
 
@@ -275,7 +278,8 @@ object ProjectMatrix {
 
     // resolve to the closest match for the given row
     private[sbt] def resolveMatch(thatRow: ProjectRow): ProjectReference =
-      rows.find(r => r.isMatch(thatRow)) match {
+      (rows.find(r => r.isMatch(thatRow)) orElse
+        rows.find(r => r.isSecondaryMatch(thatRow))) match {
         case Some(r) => LocalProject(resolveProjectIds(r))
         case _       => sys.error(s"no rows were found in $id matching $thatRow: $rows")
       }
diff --git a/src/sbt-test/projectMatrix/jvm-sandwich/build.sbt b/src/sbt-test/projectMatrix/jvm-sandwich/build.sbt
new file mode 100644
index 000000000..eb3fb0f85
--- /dev/null
+++ b/src/sbt-test/projectMatrix/jvm-sandwich/build.sbt
@@ -0,0 +1,17 @@
+val dottyVersion = "0.23.0"
+ThisBuild / resolvers += "scala-integration" at "https://scala-ci.typesafe.com/artifactory/scala-integration/"
+// TODO use 2.13.4 when it's out
+lazy val scala213 = "2.13.4-bin-aeee8f0"
+
+lazy val fooApp = (projectMatrix in file("foo-app"))
+  .dependsOn(fooCore)
+  .settings(
+    name := "app",
+  )
+  .jvmPlatform(scalaVersions = Seq(dottyVersion))
+
+lazy val fooCore = (projectMatrix in file("foo-core"))
+  .settings(
+    name := "core",
+  )
+  .jvmPlatform(scalaVersions = Seq("2.13.3", "2.12.12"))
diff --git a/src/sbt-test/projectMatrix/jvm-sandwich/project/build.properties b/src/sbt-test/projectMatrix/jvm-sandwich/project/build.properties
new file mode 100644
index 000000000..0837f7a13
--- /dev/null
+++ b/src/sbt-test/projectMatrix/jvm-sandwich/project/build.properties
@@ -0,0 +1 @@
+sbt.version=1.3.13
diff --git a/src/sbt-test/projectMatrix/jvm-sandwich/project/plugins.sbt b/src/sbt-test/projectMatrix/jvm-sandwich/project/plugins.sbt
new file mode 100644
index 000000000..c129c032b
--- /dev/null
+++ b/src/sbt-test/projectMatrix/jvm-sandwich/project/plugins.sbt
@@ -0,0 +1,6 @@
+sys.props.get("plugin.version") match {
+  case Some(x) => addSbtPlugin("com.eed3si9n" % "sbt-projectmatrix" % x)
+  case _ => sys.error("""|The system property 'plugin.version' is not defined.
+                         |Specify this property using the scriptedLaunchOpts -D.""".stripMargin)
+}
+addSbtPlugin("ch.epfl.lamp" % "sbt-dotty" % "0.4.1")
diff --git a/src/sbt-test/projectMatrix/jvm-sandwich/test b/src/sbt-test/projectMatrix/jvm-sandwich/test
new file mode 100644
index 000000000..33560c709
--- /dev/null
+++ b/src/sbt-test/projectMatrix/jvm-sandwich/test
@@ -0,0 +1,2 @@
+> fooAppJVM0_23/compile
+