diff --git a/mypy.ini b/mypy.ini
index 1a2b9ea410..3fca15c01b 100644
--- a/mypy.ini
+++ b/mypy.ini
@@ -96,3 +96,6 @@ ignore_missing_imports = True
 # https://github.com/twisted/treq/pull/366
 [mypy-treq.*]
 ignore_missing_imports = True
+
+[mypy-multipart.*]
+ignore_missing_imports = True
diff --git a/poetry.lock b/poetry.lock
index 1bae0ea388..cf56f81fe1 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,4 +1,4 @@
-# This file is automatically @generated by Poetry 1.8.2 and should not be changed by hand.
+# This file is automatically @generated by Poetry 1.5.1 and should not be changed by hand.
 
 [[package]]
 name = "annotated-types"
@@ -2039,6 +2039,20 @@ files = [
 [package.dependencies]
 six = ">=1.5"
 
+[[package]]
+name = "python-multipart"
+version = "0.0.9"
+description = "A streaming multipart parser for Python"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "python_multipart-0.0.9-py3-none-any.whl", hash = "sha256:97ca7b8ea7b05f977dc3849c3ba99d51689822fab725c3703af7c866a0c2b215"},
+    {file = "python_multipart-0.0.9.tar.gz", hash = "sha256:03f54688c663f1b7977105f021043b0793151e4cb1c1a9d4a11fc13d622c4026"},
+]
+
+[package.extras]
+dev = ["atomicwrites (==1.4.1)", "attrs (==23.2.0)", "coverage (==7.4.1)", "hatch", "invoke (==2.2.0)", "more-itertools (==10.2.0)", "pbr (==6.0.0)", "pluggy (==1.4.0)", "py (==1.11.0)", "pytest (==8.0.0)", "pytest-cov (==4.1.0)", "pytest-timeout (==2.2.0)", "pyyaml (==6.0.1)", "ruff (==0.2.1)"]
+
 [[package]]
 name = "pytz"
 version = "2022.7.1"
@@ -3187,4 +3201,4 @@ user-search = ["pyicu"]
 [metadata]
 lock-version = "2.0"
 python-versions = "^3.8.0"
-content-hash = "107c8fb5c67360340854fbdba3c085fc5f9c7be24bcb592596a914eea621faea"
+content-hash = "2971f8200039ef76c661b26ff9ef3b4487ed5b47a161352481dd73e23035f5a7"
diff --git a/pyproject.toml b/pyproject.toml
index bbf9c78420..2330a11012 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -248,6 +248,7 @@ Pympler = { version = "*", optional = true }
 parameterized = { version = ">=0.7.4", optional = true }
 idna = { version = ">=2.5", optional = true }
 pyicu = { version = ">=2.10.2", optional = true }
+python-multipart = "^0.0.9"
 
 [tool.poetry.extras]
 # NB: Packages that should be part of `pip install matrix-synapse[all]` need to be specified
diff --git a/synapse/http/client.py b/synapse/http/client.py
index 4718517c97..56ad28eabf 100644
--- a/synapse/http/client.py
+++ b/synapse/http/client.py
@@ -35,6 +35,8 @@ from typing import (
     Union,
 )
 
+import attr
+import multipart
 import treq
 from canonicaljson import encode_canonical_json
 from netaddr import AddrFormatError, IPAddress, IPSet
@@ -1006,6 +1008,130 @@ class _DiscardBodyWithMaxSizeProtocol(protocol.Protocol):
         self._maybe_fail()
 
 
+@attr.s(auto_attribs=True, slots=True)
+class MultipartResponse:
+    """
+    A small class to hold parsed values of a multipart response.
+    """
+
+    json: bytes = b"{}"
+    length: Optional[int] = None
+    content_type: Optional[bytes] = None
+    disposition: Optional[bytes] = None
+    url: Optional[bytes] = None
+
+
+class _MultipartParserProtocol(protocol.Protocol):
+    """
+    Protocol to read and parse a MSC3916 multipart/mixed response
+    """
+
+    transport: Optional[ITCPTransport] = None
+
+    def __init__(
+        self,
+        stream: ByteWriteable,
+        deferred: defer.Deferred,
+        boundary: str,
+        max_length: Optional[int],
+    ) -> None:
+        self.stream = stream
+        self.deferred = deferred
+        self.boundary = boundary
+        self.max_length = max_length
+        self.parser = None
+        self.multipart_response = MultipartResponse()
+        self.has_redirect = False
+        self.in_json = False
+        self.json_done = False
+        self.file_length = 0
+        self.total_length = 0
+        self.in_disposition = False
+        self.in_content_type = False
+
+    def dataReceived(self, incoming_data: bytes) -> None:
+        if self.deferred.called:
+            return
+
+        # we don't have a parser yet, instantiate it
+        if not self.parser:
+
+            def on_header_field(data: bytes, start: int, end: int) -> None:
+                if data[start:end] == b"Location":
+                    self.has_redirect = True
+                if data[start:end] == b"Content-Disposition":
+                    self.in_disposition = True
+                if data[start:end] == b"Content-Type":
+                    self.in_content_type = True
+
+            def on_header_value(data: bytes, start: int, end: int) -> None:
+                # the first header should be content-type for application/json
+                if not self.in_json and not self.json_done:
+                    assert data[start:end] == b"application/json"
+                    self.in_json = True
+                elif self.has_redirect:
+                    self.multipart_response.url = data[start:end]
+                elif self.in_content_type:
+                    self.multipart_response.content_type = data[start:end]
+                    self.in_content_type = False
+                elif self.in_disposition:
+                    self.multipart_response.disposition = data[start:end]
+                    self.in_disposition = False
+
+            def on_part_data(data: bytes, start: int, end: int) -> None:
+                # we've seen json header but haven't written the json data
+                if self.in_json and not self.json_done:
+                    self.multipart_response.json = data[start:end]
+                    self.json_done = True
+                # we have a redirect header rather than a file, and have already captured it
+                elif self.has_redirect:
+                    return
+                # otherwise we are in the file part
+                else:
+                    logger.info("Writing multipart file data to stream")
+                    try:
+                        self.stream.write(data[start:end])
+                    except Exception as e:
+                        logger.warning(
+                            f"Exception encountered writing file data to stream: {e}"
+                        )
+                        self.deferred.errback()
+                    self.file_length += end - start
+
+            callbacks = {
+                "on_header_field": on_header_field,
+                "on_header_value": on_header_value,
+                "on_part_data": on_part_data,
+            }
+            self.parser = multipart.MultipartParser(self.boundary, callbacks)
+
+        self.total_length += len(incoming_data)
+        if self.max_length is not None and self.total_length >= self.max_length:
+            self.deferred.errback(BodyExceededMaxSize())
+            # Close the connection (forcefully) since all the data will get
+            # discarded anyway.
+            assert self.transport is not None
+            self.transport.abortConnection()
+
+        try:
+            self.parser.write(incoming_data)  # type: ignore[attr-defined]
+        except Exception as e:
+            logger.warning(f"Exception writing to multipart parser: {e}")
+            self.deferred.errback()
+            return
+
+    def connectionLost(self, reason: Failure = connectionDone) -> None:
+        # If the maximum size was already exceeded, there's nothing to do.
+        if self.deferred.called:
+            return
+
+        if reason.check(ResponseDone):
+            self.multipart_response.length = self.file_length
+            self.deferred.callback(self.multipart_response)
+        else:
+            self.deferred.errback(reason)
+
+
 class _ReadBodyWithMaxSizeProtocol(protocol.Protocol):
     """A protocol which reads body to a stream, erroring if the body exceeds a maximum size."""
 
@@ -1091,6 +1217,32 @@ def read_body_with_max_size(
     return d
 
 
+def read_multipart_response(
+    response: IResponse, stream: ByteWriteable, boundary: str, max_length: Optional[int]
+) -> "defer.Deferred[MultipartResponse]":
+    """
+    Reads a MSC3916 multipart/mixed response and parses it, reading the file part (if it contains one) into
+    the stream passed in and returning a deferred resolving to a MultipartResponse
+
+    Args:
+        response: The HTTP response to read from.
+        stream: The file-object to write to.
+        boundary: the multipart/mixed boundary string
+        max_length: maximum allowable length of the response
+    """
+    d: defer.Deferred[MultipartResponse] = defer.Deferred()
+
+    # If the Content-Length header gives a size larger than the maximum allowed
+    # size, do not bother downloading the body.
+    if max_length is not None and response.length != UNKNOWN_LENGTH:
+        if response.length > max_length:
+            response.deliverBody(_DiscardBodyWithMaxSizeProtocol(d))
+            return d
+
+    response.deliverBody(_MultipartParserProtocol(stream, d, boundary, max_length))
+    return d
+
+
 def encode_query_args(args: Optional[QueryParams]) -> bytes:
     """
     Encodes a map of query arguments to bytes which can be appended to a URL.