diff --git a/hook.js b/hook.js
index 1752bcf..40359db 100644
--- a/hook.js
+++ b/hook.js
@@ -206,24 +206,19 @@ async function processModule ({ srcUrl, context, parentGetSource, parentResolve,
     if (isStarExportLine(n) === true) {
       const [, modFile] = n.split('* from ')
 
-      let modUrl
+      async function processSubModule (url, ctx) {
+        const setters = await processModule({ srcUrl: url, context: ctx, parentGetSource, parentResolve, excludeDefault: true })
+        for (const [name, setter] of setters.entries()) {
+          addSetter(name, setter, true)
+        }
+      }
+
       if (isBareSpecifier(modFile)) {
         // Bare specifiers need to be resolved relative to the parent module.
         const result = await parentResolve(modFile, { parentURL: srcUrl })
-        modUrl = result.url
+        await processSubModule(result.url, { ...context, format: result.format })
       } else {
-        modUrl = new URL(modFile, srcUrl).href
-      }
-
-      const setters = await processModule({
-        srcUrl: modUrl,
-        context,
-        parentGetSource,
-        parentResolve,
-        excludeDefault: true
-      })
-      for (const [name, setter] of setters.entries()) {
-        addSetter(name, setter, true)
+        await processSubModule(new URL(modFile, srcUrl).href, context)
       }
     } else {
       addSetter(n, `
diff --git a/package.json b/package.json
index 45d4a06..5625605 100644
--- a/package.json
+++ b/package.json
@@ -51,7 +51,8 @@
     "imhotap": "^2.1.0",
     "openai": "^4.47.2",
     "ts-node": "^10.9.1",
-    "typescript": "^4.7.4"
+    "typescript": "^4.7.4",
+    "vue": "^3.4.31"
   },
   "dependencies": {
     "acorn": "^8.8.2",
diff --git a/test/hook/vue-server-renderer.mjs b/test/hook/vue-server-renderer.mjs
new file mode 100644
index 0000000..2e0b3b2
--- /dev/null
+++ b/test/hook/vue-server-renderer.mjs
@@ -0,0 +1,5 @@
+// https://github.com/nodejs/import-in-the-middle/issues/139
+import { strictEqual } from 'assert'
+import * as lib from 'vue/server-renderer'
+
+strictEqual(typeof lib.renderToString, 'function')