I don't know of anyone doing rigorous studies on this. I don't know why anyone would, there is no profit motive for it.
That said, to the extent that the vaccines are the same, it shouldn't matter. To the extent that they are different, we should want to combine the effects, since we know they all work.
For myself, my first two doses were Pfizer/BioNTech. My third dose was Moderna. In terms of side effects, the third dose felt pretty much like the second.
What is the current thinking on whether it's safe and effective to get a COVID booster shot from a different vaccine than the one you originally received? For example, getting a Pfizer shot if you originally got J&J. Is it more effective than getting a booster shot of the same type you originally got? References to good papers and analyses would be appreciated.