diff --git a/main/src/main/scala/sbt/Cross.scala b/main/src/main/scala/sbt/Cross.scala
index 73b4cadec..86b31ff59 100644
--- a/main/src/main/scala/sbt/Cross.scala
+++ b/main/src/main/scala/sbt/Cross.scala
@@ -339,16 +339,18 @@ object Cross {
                 )
             }
         }
-      } else {
-        val binaryVersion = CrossVersion.binaryScalaVersion(version)
+      } else
+        // This is the default implementation for ++ <sv> <command1>
+        // It checks that <sv> is backward compatible with one of the Scala versions listed
+        // in crossScalaVersions setting. Note this must account for the fact that in Scala 3.x
+        // 3.1.0 is not compatible with 3.0.0.
         projectScalaVersions.map {
           case (project, scalaVersions) =>
-            if (scalaVersions.exists(v => CrossVersion.binaryScalaVersion(v) == binaryVersion))
+            if (scalaVersions.exists(CrossVersion.isScalaBinaryCompatibleWith(version, _)))
               (project, Some(version), scalaVersions)
             else
               (project, None, scalaVersions)
         }
-      }
     }
 
     val included = projects.collect {
diff --git a/notes/1.7.0/cross-strict-aggregation-scala-3.md b/notes/1.7.0/cross-strict-aggregation-scala-3.md
new file mode 100644
index 000000000..8e00c2422
--- /dev/null
+++ b/notes/1.7.0/cross-strict-aggregation-scala-3.md
@@ -0,0 +1,8 @@
+[@ruippeixotog]: https://github.com/ruippeixotog
+
+[#6915]: https://github.com/sbt/sbt/issues/6915
+[#6926]: https://github.com/sbt/sbt/pull/6926
+
+### Bug Fixes
+
+- Make `++ <scala-version> <command>` run `<command>` only on compatible Scala 3 subprojects. [#6915][]/[#6926][] by [@ruippeixotog][]
diff --git a/project/Dependencies.scala b/project/Dependencies.scala
index 991e96b03..6d3e3f63a 100644
--- a/project/Dependencies.scala
+++ b/project/Dependencies.scala
@@ -14,7 +14,7 @@ object Dependencies {
   // sbt modules
   private val ioVersion = nightlyVersion.getOrElse("1.6.0")
   private val lmVersion =
-    sys.props.get("sbt.build.lm.version").orElse(nightlyVersion).getOrElse("1.7.0-M1")
+    sys.props.get("sbt.build.lm.version").orElse(nightlyVersion).getOrElse("1.7.0-M3")
   val zincVersion = nightlyVersion.getOrElse("1.7.0-M2")
 
   private val sbtIO = "org.scala-sbt" %% "io" % ioVersion
diff --git a/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/build.sbt b/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/build.sbt
new file mode 100644
index 000000000..d5cf2f898
--- /dev/null
+++ b/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/build.sbt
@@ -0,0 +1,14 @@
+scalaVersion := "2.12.16"
+
+lazy val core = project
+  .settings(
+    crossScalaVersions := Seq("2.12.16", "3.0.2", "3.1.2")
+  )
+
+lazy val subproj = project
+  .dependsOn(core)
+  .settings(
+    crossScalaVersions := Seq("2.12.16", "3.1.2"),
+    // a random library compiled against Scala 3.1
+    libraryDependencies += "org.http4s" %% "http4s-core" % "0.23.12"
+  )
diff --git a/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/subproj/src/main/scala/A.scala b/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/subproj/src/main/scala/A.scala
new file mode 100644
index 000000000..da95b9fc4
--- /dev/null
+++ b/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/subproj/src/main/scala/A.scala
@@ -0,0 +1,6 @@
+import org.http4s.Uri
+
+object A {
+  // Just using something from http4s 
+  Uri.fromString("example.com")
+}
diff --git a/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/test b/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/test
new file mode 100644
index 000000000..ea7afbf93
--- /dev/null
+++ b/sbt-app/src/sbt-test/actions/cross-strict-aggregation-scala-3/test
@@ -0,0 +1,14 @@
+> ++3.0.2 compile
+
+$ exists core/target/scala-3.0.2
+-$ exists core/target/scala-3.1.2
+-$ exists subproj/target/scala-3.0.2
+-$ exists subproj/target/scala-3.1.2
+
+> clean
+> ++3.1.2 compile
+
+-$ exists core/target/scala-3.0.2
+$ exists core/target/scala-3.1.2
+-$ exists subproj/target/scala-3.0.2
+$ exists subproj/target/scala-3.1.2