diff --git a/README.md b/README.md
index e64f90cf..f7be47c9 100644
--- a/README.md
+++ b/README.md
@@ -23,6 +23,7 @@
 
 | status | `jupyterlite-pyodide-kernel` | `jupyterlite-core` |  `jupyterlab`  |   `notebook`   |  `retrolab`  |
 | :----: | :--------------------------: | :----------------: | :------------: | :------------: | :----------: |
+|  pre   |           `0.4.*`            |    `>=0.4,<0.5`    | `>=4.2.0,<4.3` | `>=7.2.0,<7.3` |      -       |
 | stable |           `0.3.*`            |    `>=0.3,<0.4`    | `>=4.1.1,<4.2` | `>=7.1.0,<7.2` |      -       |
 | stable |           `0.2.*`            |    `>=0.2,<0.3`    | `>=4.0.7,<4.1` |  `>=7.0.5,<8`  |      -       |
 | stable |           `0.1.*`            |    `>=0.1,<0.2`    |  `>=3.5,<3.6`  |       -        | `>=0.3,<0.4` |
@@ -39,6 +40,7 @@ yet work in a full, `jupyter_server`-hosted client such as JupyterLab or Noteboo
 |      `>=0.1.2,<=0.2.1`       | `0.24.*`  | `3.10.*` |   `3.1.45`   |
 |      `>=0.2.2,<=0.2.3`       | `0.25.*`  | `3.11.*` |   `3.1.46`   |
 |      `>=0.3.*,<=0.4.0`       | `0.25.*`  | `3.11.*` |   `3.1.46`   |
+|      `>=0.4.*,<=0.5.0`       | `0.25.*`  | `3.11.*` |   `3.1.46`   |
 
 Note that the Emscripten version is strict down to the bugfix version.
 
diff --git a/packages/pyodide-kernel-extension/package.json b/packages/pyodide-kernel-extension/package.json
index 931c1253..b2ee0c6e 100644
--- a/packages/pyodide-kernel-extension/package.json
+++ b/packages/pyodide-kernel-extension/package.json
@@ -48,10 +48,10 @@
   },
   "dependencies": {
     "@jupyterlab/coreutils": "^6.1.1",
-    "@jupyterlite/contents": "^0.3.0",
-    "@jupyterlite/kernel": "^0.3.0",
+    "@jupyterlite/contents": "^0.4.0-alpha.0",
+    "@jupyterlite/kernel": "^0.4.0-alpha.0",
     "@jupyterlite/pyodide-kernel": "^0.3.1",
-    "@jupyterlite/server": "^0.3.0"
+    "@jupyterlite/server": "^0.4.0-alpha.0"
   },
   "devDependencies": {
     "@jupyterlab/builder": "~4.1.1",
diff --git a/packages/pyodide-kernel/package.json b/packages/pyodide-kernel/package.json
index b477acab..82d7b2af 100644
--- a/packages/pyodide-kernel/package.json
+++ b/packages/pyodide-kernel/package.json
@@ -53,8 +53,8 @@
   },
   "dependencies": {
     "@jupyterlab/coreutils": "^6.1.1",
-    "@jupyterlite/contents": "^0.3.0",
-    "@jupyterlite/kernel": "^0.3.0",
+    "@jupyterlite/contents": "^0.4.0-alpha.0",
+    "@jupyterlite/kernel": "^0.4.0-alpha.0",
     "comlink": "^4.4.1"
   },
   "devDependencies": {
diff --git a/pyproject.toml b/pyproject.toml
index d2a79d9d..d055edd0 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -37,7 +37,7 @@ classifiers = [
     "Programming Language :: Python :: 3.12",
 ]
 dependencies = [
-    "jupyterlite-core >=0.3.0,<0.4.0",
+    "jupyterlite-core >=0.4.0a0,<0.5.0",
     "pkginfo"
 ]
 
diff --git a/yarn.lock b/yarn.lock
index e0bba5b2..998ecabb 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -2254,6 +2254,20 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@jupyter/ydoc@npm:^2.0.1":
+  version: 2.0.1
+  resolution: "@jupyter/ydoc@npm:2.0.1"
+  dependencies:
+    "@jupyterlab/nbformat": ^3.0.0 || ^4.0.0-alpha.21 || ^4.0.0
+    "@lumino/coreutils": ^1.11.0 || ^2.0.0
+    "@lumino/disposable": ^1.10.0 || ^2.0.0
+    "@lumino/signaling": ^1.10.0 || ^2.0.0
+    y-protocols: ^1.0.5
+    yjs: ^13.5.40
+  checksum: f5f29e1ff3327ebc1cf326f53634e03c4c7bf7733d235087fe26975c16eebd404f23c2f3ba88b6e04b1927846be7162b09b8b8719a4b29e51d0299c745018cbb
+  languageName: node
+  linkType: hard
+
 "@jupyterlab/application@npm:^4.1.1":
   version: 4.1.1
   resolution: "@jupyterlab/application@npm:4.1.1"
@@ -2468,7 +2482,7 @@ __metadata:
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-"@jupyterlab/coreutils@npm:^6.1.1, @jupyterlab/coreutils@npm:^6.1.5, @jupyterlab/coreutils@npm:~6.1.5":
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   version: 6.1.5
   resolution: "@jupyterlab/coreutils@npm:6.1.5"
   dependencies:
@@ -2482,6 +2496,20 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@jupyterlab/coreutils@npm:^6.2.0, @jupyterlab/coreutils@npm:~6.2.0":
+  version: 6.2.0
+  resolution: "@jupyterlab/coreutils@npm:6.2.0"
+  dependencies:
+    "@lumino/coreutils": ^2.1.2
+    "@lumino/disposable": ^2.1.2
+    "@lumino/signaling": ^2.1.2
+    minimist: ~1.2.0
+    path-browserify: ^1.0.0
+    url-parse: ~1.5.4
+  checksum: 1975f19f567b63484055b0d1d10757b2bf66274814083e50702bb6017af22341cc3f5924d0ec7da408feacd652120b476aaaf50286a5401f798f257e899aed91
+  languageName: node
+  linkType: hard
+
 "@jupyterlab/docmanager@npm:^4.1.1":
   version: 4.1.1
   resolution: "@jupyterlab/docmanager@npm:4.1.1"
@@ -2601,7 +2629,7 @@ __metadata:
   languageName: node
   linkType: hard
 
-"@jupyterlab/nbformat@npm:^3.0.0 || ^4.0.0-alpha.21 || ^4.0.0, @jupyterlab/nbformat@npm:^4.1.1, @jupyterlab/nbformat@npm:^4.1.5, @jupyterlab/nbformat@npm:~4.1.5":
+"@jupyterlab/nbformat@npm:^3.0.0 || ^4.0.0-alpha.21 || ^4.0.0, @jupyterlab/nbformat@npm:^4.1.1, @jupyterlab/nbformat@npm:^4.1.5":
   version: 4.1.5
   resolution: "@jupyterlab/nbformat@npm:4.1.5"
   dependencies:
@@ -2610,6 +2638,15 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@jupyterlab/nbformat@npm:^4.2.0, @jupyterlab/nbformat@npm:~4.2.0":
+  version: 4.2.0
+  resolution: "@jupyterlab/nbformat@npm:4.2.0"
+  dependencies:
+    "@lumino/coreutils": ^2.1.2
+  checksum: adecadcb63de48f09aeb54eebfed8b77ab322c478fd903001e09780a01e7cf68f93716a2598631d4426d8ad9d3dc6349e8892db12575f74c8daea33f63b9c111
+  languageName: node
+  linkType: hard
+
 "@jupyterlab/notebook@npm:^4.1.1":
   version: 4.1.1
   resolution: "@jupyterlab/notebook@npm:4.1.1"
@@ -2647,7 +2684,7 @@ __metadata:
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   linkType: hard
 
-"@jupyterlab/observables@npm:^5.1.1, @jupyterlab/observables@npm:~5.1.5":
+"@jupyterlab/observables@npm:^5.1.1":
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   resolution: "@jupyterlab/observables@npm:5.1.5"
   dependencies:
@@ -2660,6 +2697,19 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@jupyterlab/observables@npm:~5.2.0":
+  version: 5.2.0
+  resolution: "@jupyterlab/observables@npm:5.2.0"
+  dependencies:
+    "@lumino/algorithm": ^2.0.1
+    "@lumino/coreutils": ^2.1.2
+    "@lumino/disposable": ^2.1.2
+    "@lumino/messaging": ^2.0.1
+    "@lumino/signaling": ^2.1.2
+  checksum: 98460d55d8ac559c79be87fe5e105cc200556e87276daed739fd89e8393c74ba9b03f67c8ecf7a02e8d8ee1fd8a60031ced6c1b7884ab5f10c8bdb876f150c5f
+  languageName: node
+  linkType: hard
+
 "@jupyterlab/outputarea@npm:^4.1.1":
   version: 4.1.1
   resolution: "@jupyterlab/outputarea@npm:4.1.1"
@@ -2712,7 +2762,7 @@ __metadata:
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   linkType: hard
 
-"@jupyterlab/services@npm:^7.1.1, @jupyterlab/services@npm:~7.1.5":
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   resolution: "@jupyterlab/services@npm:7.1.5"
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-"@jupyterlab/settingregistry@npm:^4.1.1, @jupyterlab/settingregistry@npm:^4.1.5, @jupyterlab/settingregistry@npm:~4.1.5":
+"@jupyterlab/services@npm:~7.2.0":
+  version: 7.2.0
+  resolution: "@jupyterlab/services@npm:7.2.0"
+  dependencies:
+    "@jupyter/ydoc": ^2.0.1
+    "@jupyterlab/coreutils": ^6.2.0
+    "@jupyterlab/nbformat": ^4.2.0
+    "@jupyterlab/settingregistry": ^4.2.0
+    "@jupyterlab/statedb": ^4.2.0
+    "@lumino/coreutils": ^2.1.2
+    "@lumino/disposable": ^2.1.2
+    "@lumino/polling": ^2.1.2
+    "@lumino/properties": ^2.0.1
+    "@lumino/signaling": ^2.1.2
+    ws: ^8.11.0
+  checksum: edc93389913d792841b615cd0a317e16c77621cd5cb35e67c40f7a58bcf0e31c77718ae7abcf643621ba86ce78c795d6008a9413d84ecad2b42e39bd52db1447
+  languageName: node
+  linkType: hard
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   resolution: "@jupyterlab/settingregistry@npm:4.1.5"
   dependencies:
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-"@jupyterlab/statedb@npm:^4.1.1, @jupyterlab/statedb@npm:^4.1.5, @jupyterlab/statedb@npm:~4.1.5":
+"@jupyterlab/settingregistry@npm:^4.2.0, @jupyterlab/settingregistry@npm:~4.2.0":
+  version: 4.2.0
+  resolution: "@jupyterlab/settingregistry@npm:4.2.0"
+  dependencies:
+    "@jupyterlab/nbformat": ^4.2.0
+    "@jupyterlab/statedb": ^4.2.0
+    "@lumino/commands": ^2.3.0
+    "@lumino/coreutils": ^2.1.2
+    "@lumino/disposable": ^2.1.2
+    "@lumino/signaling": ^2.1.2
+    "@rjsf/utils": ^5.13.4
+    ajv: ^8.12.0
+    json5: ^2.2.3
+  peerDependencies:
+    react: ">=16"
+  checksum: fc60490e9e977e38b14b27a9e3896b47a28930a76a84888dd86180105b9ab6d1e68544f1184bdba72b4c5aa003cb13f10c8e5ca60685827fe6f893302483a109
+  languageName: node
+  linkType: hard
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+"@jupyterlab/statedb@npm:^4.1.1, @jupyterlab/statedb@npm:^4.1.5":
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   resolution: "@jupyterlab/statedb@npm:4.1.5"
   dependencies:
@@ -2763,6 +2851,19 @@ __metadata:
   languageName: node
   linkType: hard
 
+"@jupyterlab/statedb@npm:^4.2.0, @jupyterlab/statedb@npm:~4.2.0":
+  version: 4.2.0
+  resolution: "@jupyterlab/statedb@npm:4.2.0"
+  dependencies:
+    "@lumino/commands": ^2.3.0
+    "@lumino/coreutils": ^2.1.2
+    "@lumino/disposable": ^2.1.2
+    "@lumino/properties": ^2.0.1
+    "@lumino/signaling": ^2.1.2
+  checksum: 69620478aa7bf452d7440b9433b6411edef537cd7d9f72f87f70bd6fc0c8fc50003d02ab8d9d4b0746383f98cb7035b093ce5e596e6560e3c35c5a0fe434dce4
+  languageName: node
+  linkType: hard
+
 "@jupyterlab/statusbar@npm:^4.1.1":
   version: 4.1.1
   resolution: "@jupyterlab/statusbar@npm:4.1.1"
@@ -2883,47 +2984,47 @@ __metadata:
   languageName: node
   linkType: hard
 
-"@jupyterlite/contents@npm:^0.3.0":
-  version: 0.3.0
-  resolution: "@jupyterlite/contents@npm:0.3.0"
+"@jupyterlite/contents@npm:^0.4.0-alpha.0":
+  version: 0.4.0-alpha.0
+  resolution: "@jupyterlite/contents@npm:0.4.0-alpha.0"
   dependencies:
-    "@jupyterlab/nbformat": ~4.1.5
-    "@jupyterlab/services": ~7.1.5
-    "@jupyterlite/localforage": ^0.3.0
+    "@jupyterlab/nbformat": ~4.2.0
+    "@jupyterlab/services": ~7.2.0
+    "@jupyterlite/localforage": ^0.4.0-alpha.0
     "@lumino/coreutils": ^2.1.2
     "@types/emscripten": ^1.39.6
     localforage: ^1.9.0
     mime: ^3.0.0
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+  checksum: 11582d9a091848e03cef40aa285f5a3b0c7dde5abe2a773b5aba9ce89e1ecf8c39da5b1a90e7d6054fa4014d2ccfc00b21a08e7b9f5af73e5d021ad71b9eee42
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-"@jupyterlite/kernel@npm:^0.3.0":
-  version: 0.3.0
-  resolution: "@jupyterlite/kernel@npm:0.3.0"
+"@jupyterlite/kernel@npm:^0.4.0-alpha.0":
+  version: 0.4.0-alpha.0
+  resolution: "@jupyterlite/kernel@npm:0.4.0-alpha.0"
   dependencies:
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-    "@jupyterlab/observables": ~5.1.5
-    "@jupyterlab/services": ~7.1.5
+    "@jupyterlab/coreutils": ~6.2.0
+    "@jupyterlab/observables": ~5.2.0
+    "@jupyterlab/services": ~7.2.0
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     "@lumino/disposable": ^2.1.2
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-  version: 0.3.0
-  resolution: "@jupyterlite/localforage@npm:0.3.0"
+"@jupyterlite/localforage@npm:^0.4.0-alpha.0":
+  version: 0.4.0-alpha.0
+  resolution: "@jupyterlite/localforage@npm:0.4.0-alpha.0"
   dependencies:
-    "@jupyterlab/coreutils": ~6.1.5
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     localforage: ^1.9.0
     localforage-memoryStorageDriver: ^0.9.2
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@@ -2933,10 +3034,10 @@ __metadata:
   dependencies:
     "@jupyterlab/builder": ~4.1.1
     "@jupyterlab/coreutils": ^6.1.1
-    "@jupyterlite/contents": ^0.3.0
-    "@jupyterlite/kernel": ^0.3.0
+    "@jupyterlite/contents": ^0.4.0-alpha.0
+    "@jupyterlite/kernel": ^0.4.0-alpha.0
     "@jupyterlite/pyodide-kernel": ^0.3.1
-    "@jupyterlite/server": ^0.3.0
+    "@jupyterlite/server": ^0.4.0-alpha.0
     rimraf: ^5.0.1
     typescript: ~5.2.2
   languageName: unknown
@@ -2966,8 +3067,8 @@ __metadata:
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     "@jupyterlab/coreutils": ^6.1.1
     "@jupyterlab/testutils": ~4.1.1
-    "@jupyterlite/contents": ^0.3.0
-    "@jupyterlite/kernel": ^0.3.0
+    "@jupyterlite/contents": ^0.4.0-alpha.0
+    "@jupyterlite/kernel": ^0.4.0-alpha.0
     "@types/jest": ^29.5.4
     comlink: ^4.4.1
     esbuild: ^0.19.2
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-    "@jupyterlab/nbformat": ~4.1.5
-    "@jupyterlab/observables": ~5.1.5
-    "@jupyterlab/services": ~7.1.5
-    "@jupyterlab/settingregistry": ~4.1.5
-    "@jupyterlab/statedb": ~4.1.5
-    "@jupyterlite/contents": ^0.3.0
-    "@jupyterlite/kernel": ^0.3.0
-    "@jupyterlite/session": ^0.3.0
-    "@jupyterlite/settings": ^0.3.0
-    "@jupyterlite/translation": ^0.3.0
-    "@lumino/application": ^2.3.0
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+  resolution: "@jupyterlite/server@npm:0.4.0-alpha.0"
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+    "@jupyterlab/observables": ~5.2.0
+    "@jupyterlab/services": ~7.2.0
+    "@jupyterlab/settingregistry": ~4.2.0
+    "@jupyterlab/statedb": ~4.2.0
+    "@jupyterlite/contents": ^0.4.0-alpha.0
+    "@jupyterlite/kernel": ^0.4.0-alpha.0
+    "@jupyterlite/session": ^0.4.0-alpha.0
+    "@jupyterlite/settings": ^0.4.0-alpha.0
+    "@jupyterlite/translation": ^0.4.0-alpha.0
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+"@jupyterlite/session@npm:^0.4.0-alpha.0":
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+  resolution: "@jupyterlite/session@npm:0.4.0-alpha.0"
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-  resolution: "@jupyterlite/settings@npm:0.3.0"
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-  resolution: "@jupyterlite/translation@npm:0.3.0"
+"@jupyterlite/translation@npm:^0.4.0-alpha.0":
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