Is there a limit to the number of players that can by synched?

Hi folks,
Just as it says in the title. is there a limit? I currently have two SB1s; two booms; one touch; and a controller. I'm considering adding maybe another one or two players (either SB family, or something like the vidabox). the house is 'awkward' rather than 'massive'. I've tried searching but not found anything to say if there's an upper limit to how many can be synched?

I currently run LMS on a desktop PC. Presumably, if I eventually go for something like a vortexbox running LMS, to allow the PC to be switched off, then that would have no impact on this number of players?

Thanks

Donald