diff --git a/datasette/app.py b/datasette/app.py
index 4a8ead1d..16a29e20 100644
--- a/datasette/app.py
+++ b/datasette/app.py
@@ -651,9 +651,12 @@ class Datasette:
                 if not database.is_mutable:
                     await database.table_counts(limit=60 * 60 * 1000)
 
-        return AsgiLifespan(
+        asgi = AsgiLifespan(
             AsgiTracer(DatasetteRouter(self, routes)), on_startup=setup_db
         )
+        for wrapper in pm.hook.asgi_wrapper(datasette=self):
+            asgi = wrapper(asgi)
+        return asgi
 
 
 class DatasetteRouter(AsgiRouter):
diff --git a/datasette/hookspecs.py b/datasette/hookspecs.py
index 61523a31..42adaae8 100644
--- a/datasette/hookspecs.py
+++ b/datasette/hookspecs.py
@@ -5,6 +5,11 @@ hookspec = HookspecMarker("datasette")
 hookimpl = HookimplMarker("datasette")
 
 
+@hookspec
+def asgi_wrapper(datasette):
+    "Returns an ASGI middleware callable to wrap our ASGI application with"
+
+
 @hookspec
 def prepare_connection(conn):
     "Modify SQLite connection in some way e.g. register custom SQL functions"
diff --git a/docs/plugins.rst b/docs/plugins.rst
index bd32b3a6..be335546 100644
--- a/docs/plugins.rst
+++ b/docs/plugins.rst
@@ -666,3 +666,44 @@ The plugin hook can then be used to register the new facet class like this:
     @hookimpl
     def register_facet_classes():
         return [SpecialFacet]
+
+
+.. _plugin_asgi_wrapper:
+
+asgi_wrapper(datasette)
+~~~~~~~~~~~~~~~~~~~~~~~
+
+Return an `ASGI <https://asgi.readthedocs.io/>`__ middleware wrapper function that will be applied to the Datasette ASGI application.
+
+This is a very powerful hook. You can use it to manipulate the entire Datasette response, or even to configure new URL routes that will be handled by your own custom code.
+
+You can write your ASGI code directly against the low-level specification, or you can use the middleware utilites provided by an ASGI framework such as `Starlette <https://www.starlette.io/middleware/>`__.
+
+This example plugin adds a ``x-databases`` HTTP header listing the currently attached databases:
+
+.. code-block:: python
+
+    from datasette import hookimpl
+    from functools import wraps
+
+
+    @hookimpl
+    def asgi_wrapper(datasette):
+        def wrap_with_databases_header(app):
+            @wraps(app)
+            async def add_x_databases_header(scope, recieve, send):
+                async def wrapped_send(event):
+                    if event["type"] == "http.response.start":
+                        original_headers = event.get("headers") or []
+                        event = {
+                            "type": event["type"],
+                            "status": event["status"],
+                            "headers": original_headers + [
+                                [b"x-databases",
+                                ", ".join(datasette.databases.keys()).encode("utf-8")]
+                            ],
+                        }
+                    await send(event)
+                await app(scope, recieve, wrapped_send)
+            return add_x_databases_header
+        return wrap_with_databases_header
diff --git a/tests/fixtures.py b/tests/fixtures.py
index 0330c8ed..fab6509e 100644
--- a/tests/fixtures.py
+++ b/tests/fixtures.py
@@ -372,6 +372,7 @@ def render_cell(value, column, table, database, datasette):
 
 PLUGIN2 = """
 from datasette import hookimpl
+from functools import wraps
 import jinja2
 import json
 
@@ -413,6 +414,28 @@ def render_cell(value, database):
             label=jinja2.escape(data["label"] or "") or "&nbsp;"
         )
     )
+
+
+@hookimpl
+def asgi_wrapper(datasette):
+    def wrap_with_databases_header(app):
+        @wraps(app)
+        async def add_x_databases_header(scope, recieve, send):
+            async def wrapped_send(event):
+                if event["type"] == "http.response.start":
+                    original_headers = event.get("headers") or []
+                    event = {
+                        "type": event["type"],
+                        "status": event["status"],
+                        "headers": original_headers + [
+                            [b"x-databases",
+                            ", ".join(datasette.databases.keys()).encode("utf-8")]
+                        ],
+                    }
+                await send(event)
+            await app(scope, recieve, wrapped_send)
+        return add_x_databases_header
+    return wrap_with_databases_header
 """
 
 TABLES = (
diff --git a/tests/test_plugins.py b/tests/test_plugins.py
index 56033bdd..9bdd491a 100644
--- a/tests/test_plugins.py
+++ b/tests/test_plugins.py
@@ -162,3 +162,8 @@ def test_plugins_extra_body_script(app_client, path, expected_extra_body_script)
     json_data = r.search(app_client.get(path).body.decode("utf8")).group(1)
     actual_data = json.loads(json_data)
     assert expected_extra_body_script == actual_data
+
+
+def test_plugins_asgi_wrapper(app_client):
+    response = app_client.get("/fixtures")
+    assert "fixtures" == response.headers["x-databases"]