diff --git a/builtin/fetch.c b/builtin/fetch.c
index d8e798dc69..b6d45f8359 100644
--- a/builtin/fetch.c
+++ b/builtin/fetch.c
@@ -1757,7 +1757,7 @@ static int fetch_multiple(struct string_list *list, int max_children)
 		result = run_processes_parallel_tr2(max_children,
 						    &fetch_next_remote,
 						    &fetch_failed_to_start,
-						    NULL,
+						    NULL, NULL,
 						    &fetch_finished,
 						    &state,
 						    "fetch", "parallel/fetch");
diff --git a/builtin/submodule--helper.c b/builtin/submodule--helper.c
index 14f6e4ee8c..136e09a016 100644
--- a/builtin/submodule--helper.c
+++ b/builtin/submodule--helper.c
@@ -2294,7 +2294,7 @@ static int update_submodules(struct submodule_update_clone *suc)
 	int i;
 
 	run_processes_parallel_tr2(suc->max_jobs, update_clone_get_next_task,
-				   update_clone_start_failure, NULL,
+				   update_clone_start_failure, NULL, NULL,
 				   update_clone_task_finished, suc, "submodule",
 				   "parallel/update");
 
diff --git a/hook.c b/hook.c
index a509d2d80e..e16b082cbd 100644
--- a/hook.c
+++ b/hook.c
@@ -434,6 +434,7 @@ int run_hooks(const char *hookname, struct run_hooks_opt *options)
 				   pick_next_hook,
 				   notify_start_failure,
 				   options->feed_pipe,
+				   NULL,
 				   notify_hook_finished,
 				   &cb_data,
 				   "hook",
diff --git a/run-command.c b/run-command.c
index e7eeb6c49b..36a4edbacf 100644
--- a/run-command.c
+++ b/run-command.c
@@ -1559,6 +1559,7 @@ struct parallel_processes {
 	get_next_task_fn get_next_task;
 	start_failure_fn start_failure;
 	feed_pipe_fn feed_pipe;
+	consume_sideband_fn consume_sideband;
 	task_finished_fn task_finished;
 
 	struct {
@@ -1624,6 +1625,7 @@ static void pp_init(struct parallel_processes *pp,
 		    get_next_task_fn get_next_task,
 		    start_failure_fn start_failure,
 		    feed_pipe_fn feed_pipe,
+		    consume_sideband_fn consume_sideband,
 		    task_finished_fn task_finished,
 		    void *data)
 {
@@ -1644,6 +1646,7 @@ static void pp_init(struct parallel_processes *pp,
 	pp->start_failure = start_failure ? start_failure : default_start_failure;
 	pp->feed_pipe = feed_pipe ? feed_pipe : default_feed_pipe;
 	pp->task_finished = task_finished ? task_finished : default_task_finished;
+	pp->consume_sideband = consume_sideband;
 
 	pp->nr_processes = 0;
 	pp->output_owner = 0;
@@ -1680,7 +1683,10 @@ static void pp_cleanup(struct parallel_processes *pp)
 	 * When get_next_task added messages to the buffer in its last
 	 * iteration, the buffered output is non empty.
 	 */
-	strbuf_write(&pp->buffered_output, stderr);
+	if (pp->consume_sideband)
+		pp->consume_sideband(&pp->buffered_output, pp->data);
+	else
+		strbuf_write(&pp->buffered_output, stderr);
 	strbuf_release(&pp->buffered_output);
 
 	sigchain_pop_common();
@@ -1801,9 +1807,13 @@ static void pp_buffer_stderr(struct parallel_processes *pp, int output_timeout)
 static void pp_output(struct parallel_processes *pp)
 {
 	int i = pp->output_owner;
+
 	if (pp->children[i].state == GIT_CP_WORKING &&
 	    pp->children[i].err.len) {
-		strbuf_write(&pp->children[i].err, stderr);
+		if (pp->consume_sideband)
+			pp->consume_sideband(&pp->children[i].err, pp->data);
+		else
+			strbuf_write(&pp->children[i].err, stderr);
 		strbuf_reset(&pp->children[i].err);
 	}
 }
@@ -1842,11 +1852,15 @@ static int pp_collect_finished(struct parallel_processes *pp)
 			strbuf_addbuf(&pp->buffered_output, &pp->children[i].err);
 			strbuf_reset(&pp->children[i].err);
 		} else {
-			strbuf_write(&pp->children[i].err, stderr);
+			/* Output errors, then all other finished child processes */
+			if (pp->consume_sideband) {
+				pp->consume_sideband(&pp->children[i].err, pp->data);
+				pp->consume_sideband(&pp->buffered_output, pp->data);
+			} else {
+				strbuf_write(&pp->children[i].err, stderr);
+				strbuf_write(&pp->buffered_output, stderr);
+			}
 			strbuf_reset(&pp->children[i].err);
-
-			/* Output all other finished child processes */
-			strbuf_write(&pp->buffered_output, stderr);
 			strbuf_reset(&pp->buffered_output);
 
 			/*
@@ -1870,6 +1884,7 @@ int run_processes_parallel(int n,
 			   get_next_task_fn get_next_task,
 			   start_failure_fn start_failure,
 			   feed_pipe_fn feed_pipe,
+			   consume_sideband_fn consume_sideband,
 			   task_finished_fn task_finished,
 			   void *pp_cb)
 {
@@ -1880,7 +1895,7 @@ int run_processes_parallel(int n,
 
 	sigchain_push(SIGPIPE, SIG_IGN);
 
-	pp_init(&pp, n, get_next_task, start_failure, feed_pipe, task_finished, pp_cb);
+	pp_init(&pp, n, get_next_task, start_failure, feed_pipe, consume_sideband, task_finished, pp_cb);
 	while (1) {
 		for (i = 0;
 		    i < spawn_cap && !pp.shutdown &&
@@ -1918,6 +1933,7 @@ int run_processes_parallel(int n,
 int run_processes_parallel_tr2(int n, get_next_task_fn get_next_task,
 			       start_failure_fn start_failure,
 			       feed_pipe_fn feed_pipe,
+			       consume_sideband_fn consume_sideband,
 			       task_finished_fn task_finished, void *pp_cb,
 			       const char *tr2_category, const char *tr2_label)
 {
@@ -1927,7 +1943,8 @@ int run_processes_parallel_tr2(int n, get_next_task_fn get_next_task,
 				   ((n < 1) ? online_cpus() : n));
 
 	result = run_processes_parallel(n, get_next_task, start_failure,
-					feed_pipe, task_finished, pp_cb);
+					feed_pipe, consume_sideband,
+					task_finished, pp_cb);
 
 	trace2_region_leave(tr2_category, tr2_label, NULL);
 
diff --git a/run-command.h b/run-command.h
index 1e3cf0999f..ebc4a95a94 100644
--- a/run-command.h
+++ b/run-command.h
@@ -457,6 +457,20 @@ typedef int (*feed_pipe_fn)(struct strbuf *pipe,
 			    void *pp_cb,
 			    void *pp_task_cb);
 
+/**
+ * If this callback is provided, instead of collating process output to stderr,
+ * they will be collated into a new pipe. consume_sideband_fn will be called
+ * repeatedly. When output is available on that pipe, it will be contained in
+ * 'output'. But it will be called with an empty 'output' too, to allow for
+ * keepalives or similar operations if necessary.
+ *
+ * pp_cb is the callback cookie as passed into run_processes_parallel.
+ *
+ * Since this callback is provided with the collated output, no task cookie is
+ * provided.
+ */
+typedef void (*consume_sideband_fn)(struct strbuf *output, void *pp_cb);
+
 /**
  * This callback is called on every child process that finished processing.
  *
@@ -492,10 +506,12 @@ int run_processes_parallel(int n,
 			   get_next_task_fn,
 			   start_failure_fn,
 			   feed_pipe_fn,
+			   consume_sideband_fn,
 			   task_finished_fn,
 			   void *pp_cb);
 int run_processes_parallel_tr2(int n, get_next_task_fn, start_failure_fn,
-			       feed_pipe_fn, task_finished_fn, void *pp_cb,
+			       feed_pipe_fn, consume_sideband_fn,
+			       task_finished_fn, void *pp_cb,
 			       const char *tr2_category, const char *tr2_label);
 
 #endif
diff --git a/submodule.c b/submodule.c
index dc4a6a60f4..4926642451 100644
--- a/submodule.c
+++ b/submodule.c
@@ -1644,7 +1644,7 @@ int fetch_populated_submodules(struct repository *r,
 	run_processes_parallel_tr2(max_parallel_jobs,
 				   get_next_submodule,
 				   fetch_start_failure,
-				   NULL,
+				   NULL, NULL,
 				   fetch_finish,
 				   &spf,
 				   "submodule", "parallel/fetch");
diff --git a/t/helper/test-run-command.c b/t/helper/test-run-command.c
index 9348184d30..d53db6d11c 100644
--- a/t/helper/test-run-command.c
+++ b/t/helper/test-run-command.c
@@ -51,6 +51,16 @@ static int no_job(struct child_process *cp,
 	return 0;
 }
 
+static void test_consume_sideband(struct strbuf *output, void *cb)
+{
+	FILE *sideband;
+
+	sideband = fopen("./sideband", "a");
+
+	strbuf_write(output, sideband);
+	fclose(sideband);
+}
+
 static int task_finished(int result,
 			 struct strbuf *err,
 			 void *pp_cb,
@@ -201,7 +211,7 @@ static int testsuite(int argc, const char **argv)
 		suite.tests.nr, max_jobs);
 
 	ret = run_processes_parallel(max_jobs, next_test, test_failed,
-				     test_stdin, test_finished, &suite);
+				     test_stdin, NULL, test_finished, &suite);
 
 	if (suite.failed.nr > 0) {
 		ret = 1;
@@ -429,23 +439,28 @@ int cmd__run_command(int argc, const char **argv)
 
 	if (!strcmp(argv[1], "run-command-parallel"))
 		exit(run_processes_parallel(jobs, parallel_next,
-					    NULL, NULL, NULL, &proc));
+					    NULL, NULL, NULL, NULL, &proc));
 
 	if (!strcmp(argv[1], "run-command-abort"))
 		exit(run_processes_parallel(jobs, parallel_next,
-					    NULL, NULL, task_finished, &proc));
+					    NULL, NULL, NULL, task_finished, &proc));
 
 	if (!strcmp(argv[1], "run-command-no-jobs"))
 		exit(run_processes_parallel(jobs, no_job,
-					    NULL, NULL, task_finished, &proc));
+					    NULL, NULL, NULL, task_finished, &proc));
 
 	if (!strcmp(argv[1], "run-command-stdin")) {
 		proc.in = -1;
 		proc.no_stdin = 0;
 		exit (run_processes_parallel(jobs, parallel_next, NULL,
-					     test_stdin, NULL, &proc));
+					     test_stdin, NULL, NULL, &proc));
 	}
 
+	if (!strcmp(argv[1], "run-command-sideband"))
+		exit(run_processes_parallel(jobs, parallel_next, NULL, NULL,
+					    test_consume_sideband, NULL,
+					    &proc));
+
 	fprintf(stderr, "check usage\n");
 	return 1;
 }
diff --git a/t/t0061-run-command.sh b/t/t0061-run-command.sh
index 87759482ad..e99f6c7f44 100755
--- a/t/t0061-run-command.sh
+++ b/t/t0061-run-command.sh
@@ -143,6 +143,13 @@ test_expect_success 'run_command runs in parallel with more tasks than jobs avai
 	test_cmp expect actual
 '
 
+test_expect_success 'run_command can divert output' '
+	test_when_finished rm sideband &&
+	test-tool run-command run-command-sideband 3 sh -c "printf \"%s\n%s\n\" Hello World" 2>actual &&
+	test_must_be_empty actual &&
+	test_cmp expect sideband
+'
+
 cat >expect <<-EOF
 preloaded output of a child
 listening for stdin:
