I actually don't mean it as a general question. I mean it specifically for this use case, as it is an unusual request for most installations. Perhaps a switcher is really what is needed here. I'm just trying to get details as to the solution, not saying that a mixer isn't a product which shouldn't be in use. It's just an usual request and we should be certain that it's the right solution when it may not be.
A stereo receiver may be the right solution. It often has level matching, and it integrates volume control.
If source matching isn't needed, then a basic switcher may be appropriate.
Depending on the projector in use, it may have analog audio outputs with integrated volume control, so perhaps that would be a good solution.
Just trying to get more details from the OP about his specific needs.
EDIT: Keep in mind XLR and TRS connections can easily be converted to RCA and something like this allows up to 8 stereo sources to be connected to it just fine:
https://www.sweetwater.com/store/detail/RX1602
Everything playing, all at once.