That is what professionals call "aux buss"
You split the signal (on many mixers - not many dj mixers - you can switch between pre fader and post fader) and send it to a buss. All 4 channels of the DJR go to this bus and the fx pot is the gain for every channel. The aux return buss is summed with the main buss.
That is the absolute standard way of mixing effects to your main signal.