GotGame just reminded me of a sports bar I did over a dozen years ago. They had RCA and Sony DirecTV receivers, as many as four of each.

I built a box with four slots the same size as the face of a Xantech table-top IR sensor, with the slots about six inches deep, painted black on the inside. At the back of each slot was a table-top sensor wired to one particular RCA and one particular Sony satellite receiver. We used the top sensor for all the other components in the system, too. Being a sports bar, that was three large RPTVs of the same brand; I used the slots for them.

To use it, you'd put the end of the appropriate remote a half inch or more into the right slot, then push the buttons.

One RCA remote, one Sony remote, on TV remote (I've forgotten the brand).

The box had to be mounted so the slots were at an angle that was natural for holding the remotes.