Students requesting to switch partners mid term
I would consider asking the student who is not getting along with their partner, whether they would consider leaving their current partner and work on their own from here on out. That way, the student still would have to do all the work on their own, but no longer has someone benefitting from their efforts without contributing.

If the student seriously considers this solution, you can be more confident that the complaint is genuine: if the student would be willing to go it alone, it is quite likely that the contribution of their current partner is near zero. But if the student is not willing to entertain this solution as a serious option, then you can derive the information that their current partner does contribute at least something to the team, and the request looks much less reasonable.

Based on the information you retrieve from this process, you can still decide to allow the student to join a team of three, or reshuffle some other way; asking the question does not commit you to actually make the student work on their own. But it might give you relevant insights.