diff --git a/src/main/scala/sbt/internal/ProjectMatrix.scala b/src/main/scala/sbt/internal/ProjectMatrix.scala
index 603a852ff..1e426bfdd 100644
--- a/src/main/scala/sbt/internal/ProjectMatrix.scala
+++ b/src/main/scala/sbt/internal/ProjectMatrix.scala
@@ -277,6 +277,7 @@ object ProjectMatrix {
             target := base.getAbsoluteFile / "target" / svDirSuffix.dropWhile(_ == '-'),
             crossTarget := Keys.target.value,
             sourceDirectory := base.getAbsoluteFile / "src",
+            unmanagedBase := base.getAbsoluteFile / "lib",
             inConfig(Compile)(makeSources(nonScalaDirSuffix, svDirSuffix)),
             inConfig(Test)(makeSources(nonScalaDirSuffix, svDirSuffix)),
             projectDependencies := projectDependenciesTask.value,
diff --git a/src/sbt-test/projectMatrix/lib/build.sbt b/src/sbt-test/projectMatrix/lib/build.sbt
new file mode 100644
index 000000000..4ee7b633d
--- /dev/null
+++ b/src/sbt-test/projectMatrix/lib/build.sbt
@@ -0,0 +1,15 @@
+ThisBuild / version := "0.1.0-SNAPSHOT"
+
+lazy val util = projectMatrix
+  .jvmPlatform(scalaVersions = Seq("2.12.19", "2.13.13"))
+
+lazy val root = (projectMatrix in file("."))
+  .dependsOn(util)
+  .jvmPlatform(scalaVersions = Seq("2.12.19"))
+
+// ss is second system
+lazy val ss = projectMatrix
+  .dependsOn(util)
+  .jvmPlatform(scalaVersions = Seq("2.13.13"))
+
+lazy val strayJar = project
diff --git a/src/sbt-test/projectMatrix/lib/project/plugins.sbt b/src/sbt-test/projectMatrix/lib/project/plugins.sbt
new file mode 100644
index 000000000..4e80bbafc
--- /dev/null
+++ b/src/sbt-test/projectMatrix/lib/project/plugins.sbt
@@ -0,0 +1,5 @@
+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)
+}
diff --git a/src/sbt-test/projectMatrix/lib/src/main/scala/Main.scala b/src/sbt-test/projectMatrix/lib/src/main/scala/Main.scala
new file mode 100644
index 000000000..ff1427531
--- /dev/null
+++ b/src/sbt-test/projectMatrix/lib/src/main/scala/Main.scala
@@ -0,0 +1,3 @@
+object Main extends App {
+  println(com.example.Lib.getMessage)
+}
diff --git a/src/sbt-test/projectMatrix/lib/ss/src/main/scala/Main.scala b/src/sbt-test/projectMatrix/lib/ss/src/main/scala/Main.scala
new file mode 100644
index 000000000..ff1427531
--- /dev/null
+++ b/src/sbt-test/projectMatrix/lib/ss/src/main/scala/Main.scala
@@ -0,0 +1,3 @@
+object Main extends App {
+  println(com.example.Lib.getMessage)
+}
diff --git a/src/sbt-test/projectMatrix/lib/strayJar/src/main/java/com/example/Lib.java b/src/sbt-test/projectMatrix/lib/strayJar/src/main/java/com/example/Lib.java
new file mode 100644
index 000000000..3740996fa
--- /dev/null
+++ b/src/sbt-test/projectMatrix/lib/strayJar/src/main/java/com/example/Lib.java
@@ -0,0 +1,7 @@
+package com.example;
+
+public class Lib {
+    public static String getMessage() {
+        return "Hello, World!";
+    }
+}
diff --git a/src/sbt-test/projectMatrix/lib/test b/src/sbt-test/projectMatrix/lib/test
new file mode 100644
index 000000000..8a808280d
--- /dev/null
+++ b/src/sbt-test/projectMatrix/lib/test
@@ -0,0 +1,15 @@
+# debug
+#> unmanagedBase
+
+# make jar
+> strayJar/package
+
+# check root
+$ mkdir lib
+$ copy-file strayJar/target/scala-2.12/strayJar_2.12-0.1.0-SNAPSHOT.jar lib/strayJar.jar
+> root2_12/compile
+
+# check ss
+$ mkdir ss/lib
+$ copy-file strayJar/target/scala-2.12/strayJar_2.12-0.1.0-SNAPSHOT.jar ss/lib/strayJar.jar
+> ss/compile