The guy who owns the system is responsible for making sure it works right. The band collectively works on the mix. If anybody wants to play with his input going into the system (with pedals, EQs, preamps, etc.) that is their own responsibility, but it shouldn't conflict with the rest of the band's gear. Also don't expect to be a channel-hog; I get one vox channel and one instrument channel in the 5-piece group I play in. Smaller groups have more options that way usually; I get 4 channels (vox, guitar, mandolin, bodhran)in the duo. Monitor mix has to satisfy everbody.

If the venue supplies it's own system or system & sound man, everybody makes sure get there early enough for a good soundcheck and familiarization with the setup long before the gig to minimize surprises.

And I've usually got enough of my own regular crap to haul around and worry about, rather that troubling to bring along a back-up sound system too. All that should be worked out before the day of the gig.