diff --git a/changes/ip_bind_address_no_port b/changes/ip_bind_address_no_port
new file mode 100644
index 0000000000..9c4f712a9e
--- /dev/null
+++ b/changes/ip_bind_address_no_port
@@ -0,0 +1,5 @@
+  o Minor features (relays):
+    - Set the Linux-specific IP_BIND_ADDRESS_NO_PORT option on outgoing
+      sockets, allowing relays using OutboundBindAddress to make more outgoing
+      connections than ephemeral ports, as long as they are to separate
+      destinations. Related to issue 40597; patch by Alex Xu (Hello71).
diff --git a/src/core/mainloop/connection.c b/src/core/mainloop/connection.c
index 75fc3c8918..82cd19181d 100644
--- a/src/core/mainloop/connection.c
+++ b/src/core/mainloop/connection.c
@@ -2224,6 +2224,23 @@ connection_connect_sockaddr,(connection_t *conn,
              tor_socket_strerror(errno));
   }
 
+#ifdef IP_BIND_ADDRESS_NO_PORT
+  static int try_ip_bind_address_no_port = 1;
+  if (bindaddr && try_ip_bind_address_no_port &&
+      setsockopt(s, SOL_IP, IP_BIND_ADDRESS_NO_PORT, &(int){1}, sizeof(int))) {
+    if (errno == EINVAL) {
+      log_notice(LD_NET, "Tor was built with support for "
+                         "IP_BIND_ADDRESS_NO_PORT, but the current kernel "
+                         "doesn't support it. This might cause Tor to run out "
+                         "of ephemeral ports more quickly.");
+      try_ip_bind_address_no_port = 0;
+    } else {
+      log_warn(LD_NET, "Error setting IP_BIND_ADDRESS_NO_PORT on new "
+                       "connection: %s", tor_socket_strerror(errno));
+    }
+  }
+#endif
+
   if (bindaddr && bind(s, bindaddr, bindaddr_len) < 0) {
     *socket_error = tor_socket_errno(s);
     if (ERRNO_IS_EADDRINUSE(*socket_error)) {
diff --git a/src/lib/sandbox/sandbox.c b/src/lib/sandbox/sandbox.c
index 7c024d7e37..a476e57fbc 100644
--- a/src/lib/sandbox/sandbox.c
+++ b/src/lib/sandbox/sandbox.c
@@ -1033,6 +1033,14 @@ sb_setsockopt(scmp_filter_ctx ctx, sandbox_cfg_t *filter)
     return rc;
 #endif /* defined(IPV6_V6ONLY) */
 
+#ifdef IP_BIND_ADDRESS_NO_PORT
+  rc = seccomp_rule_add_2(ctx, SCMP_ACT_ALLOW, SCMP_SYS(setsockopt),
+      SCMP_CMP(1, SCMP_CMP_EQ, SOL_IP),
+      SCMP_CMP(2, SCMP_CMP_EQ, IP_BIND_ADDRESS_NO_PORT));
+  if (rc)
+    return rc;
+#endif
+
   return 0;
 }