Like Pure morning said, Seed is what this is for, but a lazy way would be to Set an initial State offset for 2 of the emitters.
This way, you can fire one emitter, and stop it at, say, frame 10, set its' initial state, then do the same for one more at a different frame, then, rewind and play, and all 3 emitters should be shooting particles all starting from different locations, i.e. locations from emitter center.
Israel "Izzy" Long
Motion and Title Design for Broadcast-Film-DS
izzylong.com