diff --git a/independent-projects/resteasy-reactive/client/runtime/src/main/java/org/jboss/resteasy/reactive/client/impl/multipart/QuarkusMultipartFormUpload.java b/independent-projects/resteasy-reactive/client/runtime/src/main/java/org/jboss/resteasy/reactive/client/impl/multipart/QuarkusMultipartFormUpload.java
index c784f8034367e..afa17ac4f1757 100644
--- a/independent-projects/resteasy-reactive/client/runtime/src/main/java/org/jboss/resteasy/reactive/client/impl/multipart/QuarkusMultipartFormUpload.java
+++ b/independent-projects/resteasy-reactive/client/runtime/src/main/java/org/jboss/resteasy/reactive/client/impl/multipart/QuarkusMultipartFormUpload.java
@@ -16,6 +16,7 @@
 import io.vertx.core.Vertx;
 import io.vertx.core.buffer.Buffer;
 import io.vertx.core.http.impl.headers.HeadersAdaptor;
+import io.vertx.core.streams.Pipe;
 import io.vertx.core.streams.ReadStream;
 import io.vertx.core.streams.impl.InboundBuffer;
 import java.io.File;
@@ -231,4 +232,15 @@ public synchronized QuarkusMultipartFormUpload endHandler(Handler<Void> handler)
         return this;
     }
 
+    /**
+     * The reason we need a custom Pipe here is that if we don't manually throttle the read stream,
+     * the fact that the underlying connection is shared can lead to exhaustion of heap memory.
+     * See <a href="https://github.com/eclipse-vertx/vert.x/issues/4473">this</a> for more details.
+     */
+    @Override
+    public Pipe<Buffer> pipe() {
+        pause();
+        return new RequestTrackingPipe<>(this, 16);
+    }
+
 }
diff --git a/independent-projects/resteasy-reactive/client/runtime/src/main/java/org/jboss/resteasy/reactive/client/impl/multipart/RequestTrackingPipe.java b/independent-projects/resteasy-reactive/client/runtime/src/main/java/org/jboss/resteasy/reactive/client/impl/multipart/RequestTrackingPipe.java
new file mode 100644
index 0000000000000..21de9d8b06da2
--- /dev/null
+++ b/independent-projects/resteasy-reactive/client/runtime/src/main/java/org/jboss/resteasy/reactive/client/impl/multipart/RequestTrackingPipe.java
@@ -0,0 +1,171 @@
+package org.jboss.resteasy.reactive.client.impl.multipart;
+
+import io.vertx.core.AsyncResult;
+import io.vertx.core.Future;
+import io.vertx.core.Handler;
+import io.vertx.core.Promise;
+import io.vertx.core.VertxException;
+import io.vertx.core.streams.Pipe;
+import io.vertx.core.streams.ReadStream;
+import io.vertx.core.streams.WriteStream;
+import java.util.concurrent.atomic.AtomicLong;
+
+/**
+ * Based on {@link io.vertx.core.streams.impl.PipeImpl}.
+ * We can't use the aforementioned class as it is not open enough for us to add the read tracking we want.
+ */
+class RequestTrackingPipe<T> implements Pipe<T> {
+
+    private final long maxInFlightReads;
+
+    private final Promise<Void> result;
+    private final ReadStream<T> src;
+    private boolean endOnSuccess = true;
+    private boolean endOnFailure = true;
+    private WriteStream<T> dst;
+
+    private boolean manuallyPaused = false;
+
+    private final AtomicLong inFlightReads = new AtomicLong(0);
+
+    public RequestTrackingPipe(ReadStream<T> src, long maxInFlightReads) {
+        this.src = src;
+        this.maxInFlightReads = maxInFlightReads;
+        this.result = Promise.promise();
+
+        // Set handlers now
+        src.endHandler(result::tryComplete);
+        src.exceptionHandler(result::tryFail);
+    }
+
+    @Override
+    public synchronized Pipe<T> endOnFailure(boolean end) {
+        endOnFailure = end;
+        return this;
+    }
+
+    @Override
+    public synchronized Pipe<T> endOnSuccess(boolean end) {
+        endOnSuccess = end;
+        return this;
+    }
+
+    @Override
+    public synchronized Pipe<T> endOnComplete(boolean end) {
+        endOnSuccess = end;
+        endOnFailure = end;
+        return this;
+    }
+
+    private void handleWriteResult(AsyncResult<Void> ack) {
+        long currentInFlightReads = inFlightReads.decrementAndGet();
+        if (currentInFlightReads <= (maxInFlightReads / 2)) {
+            synchronized (RequestTrackingPipe.this) {
+                if (manuallyPaused) {
+                    manuallyPaused = false;
+                    src.resume();
+                }
+            }
+        }
+        if (ack.failed()) {
+            result.tryFail(new WriteException(ack.cause()));
+        }
+    }
+
+    @Override
+    public void to(WriteStream<T> ws, Handler<AsyncResult<Void>> completionHandler) {
+        if (ws == null) {
+            throw new NullPointerException();
+        }
+        boolean endOnSuccess;
+        boolean endOnFailure;
+        synchronized (RequestTrackingPipe.this) {
+            if (dst != null) {
+                throw new IllegalStateException();
+            }
+            dst = ws;
+            endOnSuccess = this.endOnSuccess;
+            endOnFailure = this.endOnFailure;
+        }
+        Handler<Void> drainHandler = v -> src.resume();
+        src.handler(item -> {
+            ws.write(item, this::handleWriteResult);
+            long currentInFlightReads = inFlightReads.incrementAndGet();
+            if (ws.writeQueueFull()) {
+                src.pause();
+                ws.drainHandler(drainHandler);
+            } else if (currentInFlightReads > maxInFlightReads) {
+                synchronized (RequestTrackingPipe.this) {
+                    src.pause();
+                    manuallyPaused = true;
+                }
+            }
+        });
+        src.resume();
+        result.future().onComplete(ar -> {
+            try {
+                src.handler(null);
+            } catch (Exception ignore) {
+            }
+            try {
+                src.exceptionHandler(null);
+            } catch (Exception ignore) {
+            }
+            try {
+                src.endHandler(null);
+            } catch (Exception ignore) {
+            }
+            if (ar.succeeded()) {
+                handleSuccess(completionHandler);
+            } else {
+                Throwable err = ar.cause();
+                if (err instanceof WriteException) {
+                    src.resume();
+                    err = err.getCause();
+                }
+                handleFailure(err, completionHandler);
+            }
+        });
+    }
+
+    private void handleSuccess(Handler<AsyncResult<Void>> completionHandler) {
+        if (endOnSuccess) {
+            dst.end(completionHandler);
+        } else {
+            completionHandler.handle(Future.succeededFuture());
+        }
+    }
+
+    private void handleFailure(Throwable cause, Handler<AsyncResult<Void>> completionHandler) {
+        Future<Void> res = Future.failedFuture(cause);
+        if (endOnFailure) {
+            dst.end(ignore -> {
+                completionHandler.handle(res);
+            });
+        } else {
+            completionHandler.handle(res);
+        }
+    }
+
+    public void close() {
+        synchronized (this) {
+            src.exceptionHandler(null);
+            src.handler(null);
+            if (dst != null) {
+                dst.drainHandler(null);
+                dst.exceptionHandler(null);
+            }
+        }
+        VertxException err = new VertxException("Pipe closed", true);
+        if (result.tryFail(err)) {
+            src.resume();
+        }
+    }
+
+    private static class WriteException extends VertxException {
+        private WriteException(Throwable cause) {
+            super(cause, true);
+        }
+    }
+
+}