This could be a "hilarious" use of the Decision Review System, but nonetheless I want to know if it is possible.
Suppose both the batsmen run to the same end (mix-up, as commentators like to call it), and the fielding side puts down the wicket at one end. The on-field umpire declares one of the batsmen out. Can this batsman invoke DRS to challenge the umpire's decision, in effect, claiming that his partner should be out instead?
A non-hilarious scenario would be if a top-order batsman and a tailender gets involved in the mix-up, and the tailender is given out. The fielding captain might want to invoke the DRS to try to get the more skilled batsman out instead.