diff --git a/changelog.d/11885.feature b/changelog.d/11885.feature
new file mode 100644
index 000000000000..dde48bdd76a1
--- /dev/null
+++ b/changelog.d/11885.feature
@@ -0,0 +1 @@
+Support [MSC3667](https://github.com/matrix-org/matrix-doc/pull/3667) in a new room version.
\ No newline at end of file
diff --git a/synapse/api/room_versions.py b/synapse/api/room_versions.py
index 3f85d61b4633..432a8027c9c2 100644
--- a/synapse/api/room_versions.py
+++ b/synapse/api/room_versions.py
@@ -84,6 +84,8 @@ class RoomVersion:
     # MSC3787: Adds support for a `knock_restricted` join rule, mixing concepts of
     # knocks and restricted join rules into the same join condition.
     msc3787_knock_restricted_join_rule: bool
+    # MSC3667: Treat string format power levels as invalid, thus denied.
+    msc3667_int_only_power_levels: bool
 
 
 class RoomVersions:
@@ -103,6 +105,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V2 = RoomVersion(
         "2",
@@ -120,6 +123,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V3 = RoomVersion(
         "3",
@@ -137,6 +141,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V4 = RoomVersion(
         "4",
@@ -154,6 +159,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V5 = RoomVersion(
         "5",
@@ -171,6 +177,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V6 = RoomVersion(
         "6",
@@ -188,6 +195,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     MSC2176 = RoomVersion(
         "org.matrix.msc2176",
@@ -205,6 +213,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V7 = RoomVersion(
         "7",
@@ -222,6 +231,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V8 = RoomVersion(
         "8",
@@ -239,6 +249,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     V9 = RoomVersion(
         "9",
@@ -256,6 +267,7 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     MSC2716v3 = RoomVersion(
         "org.matrix.msc2716v3",
@@ -273,6 +285,7 @@ class RoomVersions:
         msc2716_historical=True,
         msc2716_redactions=True,
         msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=False,
     )
     MSC3787 = RoomVersion(
         "org.matrix.msc3787",
@@ -290,6 +303,45 @@ class RoomVersions:
         msc2716_historical=False,
         msc2716_redactions=False,
         msc3787_knock_restricted_join_rule=True,
+        msc3667_int_only_power_levels=False,
+    )
+    MSC3667 = RoomVersion(
+        # v7 + MSC3667
+        "org.matrix.msc3667",
+        RoomDisposition.UNSTABLE,
+        EventFormatVersions.V3,
+        StateResolutionVersions.V2,
+        enforce_key_validity=True,
+        special_case_aliases_auth=False,
+        strict_canonicaljson=True,
+        limit_notifications_power_levels=True,
+        msc2176_redaction_rules=False,
+        msc3083_join_rules=False,
+        msc3375_redaction_rules=False,
+        msc2403_knocking=True,
+        msc2716_historical=False,
+        msc2716_redactions=False,
+        msc3787_knock_restricted_join_rule=False,
+        msc3667_int_only_power_levels=True,
+    )
+    MSC3604Opt4 = RoomVersion(
+        # v9 + MSC3667 + MSC3787
+        "org.matrix.msc3604.opt4",
+        RoomDisposition.UNSTABLE,
+        EventFormatVersions.V3,
+        StateResolutionVersions.V2,
+        enforce_key_validity=True,
+        special_case_aliases_auth=False,
+        strict_canonicaljson=True,
+        limit_notifications_power_levels=True,
+        msc2176_redaction_rules=False,
+        msc3083_join_rules=True,
+        msc3375_redaction_rules=True,
+        msc2403_knocking=True,
+        msc2716_historical=False,
+        msc2716_redactions=False,
+        msc3787_knock_restricted_join_rule=True,
+        msc3667_int_only_power_levels=True,
     )
 
 
@@ -308,6 +360,8 @@ class RoomVersions:
         RoomVersions.V9,
         RoomVersions.MSC2716v3,
         RoomVersions.MSC3787,
+        RoomVersions.MSC3667,
+        RoomVersions.MSC3604Opt4,
     )
 }
 
diff --git a/synapse/event_auth.py b/synapse/event_auth.py
index 4c0b587a7643..bbf50d79767e 100644
--- a/synapse/event_auth.py
+++ b/synapse/event_auth.py
@@ -143,6 +143,22 @@ def check_auth_rules_for_event(
     Raises:
         AuthError if the checks fail
     """
+    # Before we get too far into event auth, validate that the event is even
+    # valid enough to be used
+    if event.type == EventTypes.PowerLevels:
+        # If applicable, validate that the known power levels are integers
+        if room_version_obj.msc3667_int_only_power_levels:
+            for k, v in event.content.items():
+                if k in ["events", "notifications", "users"]:
+                    if type(v) is not dict:
+                        raise AuthError(403, "Not a valid object: %s" % (k,))
+                    for v2 in v.values():
+                        if type(v2) is not int:
+                            raise AuthError(403, "Not a valid power level: %s" % (v2,))
+                else:
+                    if type(v) is not int:
+                        raise AuthError(403, "Not a valid power level: %s" % (v,))
+
     # We need to ensure that the auth events are actually for the same room, to
     # stop people from using powers they've been granted in other rooms for
     # example.