EDIT
Just a quick update as I checked what I have on my bass on the moment as an example. I have strings of gauge 35, 55, 70, 90 (If I remember rightly) tuned to EADG. I prefer really light strings for ease of bends (yes, on bass...) and slap bass, but it does mean I won't be able to drop the tuning too far. What I mean about the setup is that the action and such is set up for these very thin strings, and trying to drop the tuning will make them far too loose to play properly and will sound dreadful.
For comparison I also have a really old bass on BEAD tuning. The thicknesses there are something like 75, 95, 110, 130 (they're really old so can't remember exactly). I would not want to push them into higher tunings really as they are already pretty tight. I don't really play this one that much. I might change it to DADG or something instead as I rarely use C# or lower.
This means my two different basses have totally different actions, bridge settings and the second has an adjusted nut to accout for the thicker strings. Rather than trying to have one bass in the middle to try and cover both it's far easier to have two. The first is a (soon to be replaced) Fender P Bass and the second a cheap Ibanez BTB200, and realistically I never gig with the BTB.
This is quite a bass-heavy answer, so I texted my guitarist mates to see what they said. One generally doesn't change tuning, but has a cheap second guitar (his first one that got replaced recently) if he really needed to. Another doesn't go far enough from EADGBE to really need a second, but he does drop the low E to a D occasionally. He prefers to use a capo and find other ways of playing the chords. He said he would like to, but the second guitar would have to be gig-worthy. He often uses weird tunings on an accoustic to experiment though.
The basics of setup will carry over from bass, but I'm aware alot of these tunings are based on the open string notes, which I avoid at all costs on bass unless truly necessary, having lots of song specific tunings are perhaps unecessary. Hopefully there is some use to be found in all this.