This paper examines a supersonic multi-jet interaction problem that we believe is likely to be important for mixing enhancement and noise reduction in supersonic mixer-ejector nozzles. We demonstrate that it is possible to synchronize the screech instability of four rectangular jets by precisely adjusting the inter-jet spacing. Our experimental data agree with a theory that assumes that the phase-locking of adjacent jets occurs through a coupling at the jet lip. Although synchronization does not change the frequency of the screech tone, its amplitude is augmented. The synchronized multi-jets exhibit higher spreading than the unsynchronized jets, with the single jet spreading the least. We compare the near-field noise of the four jets with synchronized screech to the noise of the sum of four jets operated individually. Our noise measurements reveal that the more rapid mixing of the synchronized multi-jets causes the peak jet noise source to move upstream and to radiate noise at larger angles to the flow direction. Based on our results, we have grounds to believe that screech synchronization is advantageous for noise reduction internal to a mixer-ejector nozzle, since the noise can now be suppressed by a shorter acoustically lined ejector.