diff --git a/crates/ui-egui/src/opening.rs b/crates/ui-egui/src/opening.rs
index 1a816f2d8..fb2949dd4 100644
--- a/crates/ui-egui/src/opening.rs
+++ b/crates/ui-egui/src/opening.rs
@@ -132,6 +132,10 @@ pub fn poll(app: &mut VectorcraftApp) {
             app.ui.status.clear();
         }
         p.scope.run(|| finish(app, &p.path, r));
+        // A file that opened and asks about its links or fonts holds back the others too.
+        if !may_switch(app) {
+            return;
+        }
     }
 }
 
diff --git a/crates/ui-egui/src/opening/tests.rs b/crates/ui-egui/src/opening/tests.rs
index ee5d0a224..fa90d3cd5 100644
--- a/crates/ui-egui/src/opening/tests.rs
+++ b/crates/ui-egui/src/opening/tests.rs
@@ -359,14 +359,19 @@ fn a_queued_reopen_that_asks_holds_back_files_ready_to_open() {
     std::fs::create_dir_all(&dir).unwrap();
     let mut app = VectorcraftApp::new(Session::new(), Services::default());
     app.services.read = Some(Box::new(|p: &str| std::fs::read(p).map_err(|e| e.to_string())));
-    let doc = dir.join("doc.vectorcraft").to_string_lossy().into_owned();
+    let (doc, other) = (dir.join("doc.vectorcraft"), dir.join("other.vectorcraft"));
+    let (doc, other) = (doc.to_string_lossy().into_owned(), other.to_string_lossy().into_owned());
     app.run("file.new", json!({"width": 400, "height": 300})).unwrap();
     app.run("text.create", json!({"x": 10, "y": 40, "text": "Type", "font": "No Such Font Family"})).unwrap();
     app.run("document.save", json!({"path": doc})).unwrap();
     app.run("file.new", json!({})).unwrap();
+    app.run("document.save", json!({"path": other})).unwrap();
+    app.run("file.new", json!({})).unwrap();
     app.ui.dialog = Some(crate::state::Dialog::new(crate::dialogs::save_options::KIND, json!({})));
     crate::io::open_reporting(&mut app, &doc).unwrap();
-    assert_eq!(app.opening.activate.len(), 1);
+    crate::io::open_reporting(&mut app, &other).unwrap();
+    assert_eq!(app.opening.activate.len(), 2);
+    app.session.execute("file.close", &json!({"index": 1})).unwrap();
     app.session.execute("file.close", &json!({"index": 0})).unwrap();
     start(&mut app, "/art/Other.vectorcraft", vectorcraft_format::save(&vectorcraft_doc::Document::new(120.0, 80.0), false)).unwrap();
     // Time for the other file to be read; it waits for the dialog meanwhile.
@@ -380,6 +385,33 @@ fn a_queued_reopen_that_asks_holds_back_files_ready_to_open() {
     poll(&mut app);
     assert_eq!(app.ui.dialog.as_ref().map(|d| d.kind.as_str()), Some(crate::dialogs::missing_fonts::KIND));
     assert_eq!(app.session.doc().unwrap().path.as_deref(), Some(&*doc), "the dialog's document stays active");
+    assert_eq!(app.opening.activate.first().map(|(p, _)| p), Some(&other), "the later activation waits");
     assert_eq!(app.opening.pending.len(), 1, "the other file waits");
     let _ = std::fs::remove_dir_all(dir);
 }
+
+/// Of two files read off the UI thread and ready in the same frame, the first that opens and asks
+/// about its fonts holds back the second, so the question acts on its own document (#5369).
+#[test]
+fn a_file_that_opens_and_asks_holds_back_the_next_one_ready() {
+    let mut app = VectorcraftApp::new(Session::new(), Services::default());
+    app.run("file.new", json!({"width": 400, "height": 300})).unwrap();
+    app.run("text.create", json!({"x": 10, "y": 40, "text": "Type", "font": "No Such Font Family"})).unwrap();
+    let asks = vectorcraft_format::save(&app.session.doc().unwrap().doc, false);
+    app.session.execute("file.close", &json!({})).unwrap();
+    app.ui.dialog = Some(crate::state::Dialog::new(crate::dialogs::save_options::KIND, json!({})));
+    start(&mut app, "/art/Asks.vectorcraft", asks).unwrap();
+    start(&mut app, "/art/Plain.vectorcraft", vectorcraft_format::save(&vectorcraft_doc::Document::new(120.0, 80.0), false)).unwrap();
+    // Time for both files to be read; they wait for the dialog meanwhile.
+    let t0 = std::time::Instant::now();
+    while t0.elapsed().as_millis() < 500 {
+        poll(&mut app);
+        std::thread::yield_now();
+    }
+    assert_eq!(app.opening.pending.len(), 2);
+    app.ui.dialog = None;
+    poll(&mut app);
+    assert_eq!(app.ui.dialog.as_ref().map(|d| d.kind.as_str()), Some(crate::dialogs::missing_fonts::KIND));
+    assert_eq!(app.session.doc().unwrap().path.as_deref(), Some("/art/Asks.vectorcraft"), "the dialog's document stays active");
+    assert_eq!(app.opening.pending.len(), 1, "the next file waits");
+}