diff --git a/.github/workflows/check.yaml b/.github/workflows/check.yaml
index 5e495e0f..b719af1a 100644
--- a/.github/workflows/check.yaml
+++ b/.github/workflows/check.yaml
@@ -1,5 +1,7 @@
 name: Check
 
+# TODO fail-fast or whatever it's called
+
 on:
   workflow_dispatch:
   pull_request:
@@ -9,23 +11,40 @@ on:
 jobs:
   check:
     runs-on: macos-latest
-    # TODO Xcode versions (multiple?)
+    strategy:
+      fail-fast: false
+      matrix:
+        xcode-version: [15.3, 16-beta]
     steps:
       - uses: actions/checkout@v4
+      - uses: maxim-lobanov/setup-xcode@v1
+        with:
+          xcode-version: ${{ matrix.xcode-version }}
+
       - run: npm ci
+
       - run: script/format/check
       - run: script/lint/check
+
       # https://forums.swift.org/t/warnings-as-errors-for-libraries-frameworks/58393/2
       - run: swift build -Xswiftc -warnings-as-errors
       - run: swift test
 
   check-on-platforms:
     runs-on: macos-latest
+
     strategy:
+      fail-fast: false
       matrix:
+        xcode-version: [15.3, 16-beta]
         platform: [macOS, iOS, tvOS]
+
     steps:
       - uses: actions/checkout@v4
+      - uses: maxim-lobanov/setup-xcode@v1
+        with:
+          xcode-version: ${{ matrix.xcode-version }}
+
       # TODO OS version, and ambiguity in platforms, and no match
       - run: xcodebuild -scheme AblyChat -destination "platform=${{ matrix.platform }}"
       - run: xcodebuild test -scheme AblyChat -destination "platform=${{ matrix.platform }}"
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index e985a744..e934b20d 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -31,3 +31,7 @@ and then we also take the minimum of these and ably-cocoa (which at time of writ
 TODO let's see what Xcode 16 says too though — OK, doesn’t seem any different in Beta 3
 
 TODO we probably also have to take into account which simulators are available on the version of Xcode we're using, _and_ which are installed on the GitHub runner
+
+## Xcode versions
+
+TODO explain how we choose which Xcode version to test on
diff --git a/README.md b/README.md
index e2fe0322..dcd34e03 100644
--- a/README.md
+++ b/README.md
@@ -4,4 +4,4 @@ TODO
 
 ## Requirements
 
-- Swift 5.10 (that is, Xcode 15.3) or later
+- Swift 5.10 (that is, Xcode 15.3) or later (TODO choose what's right to use here)