I am not an expert, but the following seems to me to be true based on logic and a vivid imagination
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If you have a system that puts 3000 lux on a particular spot, then three of them will put 9000 on that spot, IF and only if they are all focused (beams are centered) on that spot. But change your distance from that where all the beams coincide and now you have less than three times the light you would have - you'd have to refocus to the new distance.
If you look at multi-emitter lights, all the emitters are firing straight out of the front of the light. So they will put more light on any particular point than a single emitter light of the same type, reflector size, drive etc would. But not, say, 3 times the brightness on any particular spot for a 3 emitter light.
As you get out to the point where the hot spots overlap, then things look a little better. It might be closer to 3x, but I doubt it would ever reach 3x.