diff --git a/CHANGES/11857.bugfix.rst b/CHANGES/11857.bugfix.rst
new file mode 100644
index 00000000000..7933efeb074
--- /dev/null
+++ b/CHANGES/11857.bugfix.rst
@@ -0,0 +1 @@
+Fixed multipart reading failing when encountering an empty body part -- by :user:`Dreamsorcerer`.
diff --git a/CHANGES/11862.bugfix.rst b/CHANGES/11862.bugfix.rst
new file mode 100644
index 00000000000..c2ce176c2c3
--- /dev/null
+++ b/CHANGES/11862.bugfix.rst
@@ -0,0 +1 @@
+A test for websocket parser was marked to fail, which was actually failing because the parser wasn't raising an exception for a continuation frame when there was no initial frame in context.
diff --git a/CONTRIBUTORS.txt b/CONTRIBUTORS.txt
index 3a570dc90e7..16889761889 100644
--- a/CONTRIBUTORS.txt
+++ b/CONTRIBUTORS.txt
@@ -251,6 +251,7 @@ Marco Paolini
 Marcus Stojcevich
 Mariano Anaya
 Mariusz Masztalerczuk
+Mark Larah
 Marko Kohtala
 Martijn Pieters
 Martin Melka
diff --git a/aiohttp/_websocket/reader_py.py b/aiohttp/_websocket/reader_py.py
index e0088a47af8..433591bde9d 100644
--- a/aiohttp/_websocket/reader_py.py
+++ b/aiohttp/_websocket/reader_py.py
@@ -200,6 +200,13 @@ def _handle_frame(
     ) -> None:
         msg: WSMessage
         if opcode in {OP_CODE_TEXT, OP_CODE_BINARY, OP_CODE_CONTINUATION}:
+            # Validate continuation frames before processing
+            if opcode == OP_CODE_CONTINUATION and self._opcode == OP_CODE_NOT_SET:
+                raise WebSocketError(
+                    WSCloseCode.PROTOCOL_ERROR,
+                    "Continuation frame for non started message",
+                )
+
             # load text/binary
             if not fin:
                 # got partial frame payload
@@ -216,11 +223,6 @@ def _handle_frame(
 
             has_partial = bool(self._partial)
             if opcode == OP_CODE_CONTINUATION:
-                if self._opcode == OP_CODE_NOT_SET:
-                    raise WebSocketError(
-                        WSCloseCode.PROTOCOL_ERROR,
-                        "Continuation frame for non started message",
-                    )
                 opcode = self._opcode
                 self._opcode = OP_CODE_NOT_SET
             # previous frame was non finished
diff --git a/aiohttp/multipart.py b/aiohttp/multipart.py
index 15901e89e0a..a2848f5a486 100644
--- a/aiohttp/multipart.py
+++ b/aiohttp/multipart.py
@@ -375,7 +375,8 @@ async def _read_chunk_from_stream(self, size: int) -> bytes:
         ), "Chunk size must be greater or equal than boundary length + 2"
         first_chunk = self._prev_chunk is None
         if first_chunk:
-            self._prev_chunk = await self._content.read(size)
+            # We need to re-add the CRLF that got removed from headers parsing.
+            self._prev_chunk = b"\r\n" + await self._content.read(size)
 
         chunk = b""
         # content.read() may return less than size, so we need to loop to ensure
@@ -402,12 +403,11 @@ async def _read_chunk_from_stream(self, size: int) -> bytes:
             with warnings.catch_warnings():
                 warnings.filterwarnings("ignore", category=DeprecationWarning)
                 self._content.unread_data(window[idx:])
-            if size > idx:
-                self._prev_chunk = self._prev_chunk[:idx]
+            self._prev_chunk = self._prev_chunk[:idx]
             chunk = window[len(self._prev_chunk) : idx]
             if not chunk:
                 self._at_eof = True
-        result = self._prev_chunk
+        result = self._prev_chunk[2 if first_chunk else 0 :]  # Strip initial CRLF
         self._prev_chunk = chunk
         return result
 
@@ -772,7 +772,7 @@ async def _read_headers(self) -> "CIMultiDictProxy[str]":
         lines = []
         while True:
             chunk = await self._content.readline()
-            chunk = chunk.strip()
+            chunk = chunk.rstrip(b"\r\n")
             lines.append(chunk)
             if not chunk:
                 break
diff --git a/tests/test_multipart.py b/tests/test_multipart.py
index fcceec12396..14896667e52 100644
--- a/tests/test_multipart.py
+++ b/tests/test_multipart.py
@@ -932,6 +932,33 @@ async def test_reading_skips_prelude(self) -> None:
             assert first.at_eof()
             assert not second.at_eof()
 
+    async def test_read_empty_body_part(self) -> None:
+        with Stream(b"--:\r\n\r\n--:--") as stream:
+            reader = aiohttp.MultipartReader(
+                {CONTENT_TYPE: 'multipart/related;boundary=":"'},
+                stream,
+            )
+            body_parts = []
+            async for part in reader:
+                assert isinstance(part, BodyPartReader)
+                body_parts.append(await part.read())
+
+        assert body_parts == [b""]
+
+    async def test_read_body_part_headers_only(self) -> None:
+        with Stream(b"--:\r\nContent-Type: text/plain\r\n\r\n--:--") as stream:
+            reader = aiohttp.MultipartReader(
+                {CONTENT_TYPE: 'multipart/related;boundary=":"'},
+                stream,
+            )
+            body_parts = []
+            async for part in reader:
+                assert isinstance(part, BodyPartReader)
+                assert "Content-Type" in part.headers
+                body_parts.append(await part.read())
+
+        assert body_parts == [b""]
+
     async def test_read_form_default_encoding(self) -> None:
         with Stream(
             b"--:\r\n"
diff --git a/tests/test_websocket_parser.py b/tests/test_websocket_parser.py
index ce181b43f73..6de09a2cb00 100644
--- a/tests/test_websocket_parser.py
+++ b/tests/test_websocket_parser.py
@@ -236,12 +236,11 @@ def test_parse_frame_header_control_frame(
         parser.parse_frame(struct.pack("!BB", 0b00001000, 0b00000000))
 
 
-@pytest.mark.xfail()
-def test_parse_frame_header_new_data_err(
-    out: WebSocketDataQueue, parser: PatchableWebSocketReader
-) -> None:
-    with pytest.raises(WebSocketError):
-        parser.parse_frame(struct.pack("!BB", 0b000000000, 0b00000000))
+def test_parse_frame_header_new_data_err(parser: PatchableWebSocketReader) -> None:
+    with pytest.raises(WebSocketError) as msg:
+        parser._feed_data(struct.pack("!BB", 0b00000000, 0b00000000))
+    assert msg.value.code == WSCloseCode.PROTOCOL_ERROR
+    assert str(msg.value) == "Continuation frame for non started message"
 
 
 def test_parse_frame_header_payload_size(