Re: 2 vive systems in same big room creates base station conflict
Two base stations is actually the answer. If you have four (4) base stations set up, that's too many!
To make this work, you should...
1) Set up two base stations surrounding your play area (where you intend to use the Vives). The other two can stay untouched as spares!
2) Configure the first Vive by running room scale setup. (While you do this, make sure the second Vive is completely turned off, or you might pair it by mistake.)
3) Once you've set up the first Vive, quit SteamVR and make sure it's totally powered down.
4) Then on your second PC, configure your second Vive. You'll be using the same base stations as before, which should register fine with the second Vive. Once everything is paired, you should be able to power on and use both Vives at once.
As we always point out, be careful with two people in the same play space! For seated games this isn't usually a problem, but for apps that make you move around, be careful about people running into each other.