Sharing space with another WC group would be gutsy. I can think of two ways you might approach it. One would be to train at different times, to have a as little contact with the other group as possible, and have a standing rule for students not to talk about or compare techniques with the other group , period.
That wouldn't work for me though, or my (last remaining) students. They are a curious bunch and they are always asking questions about stuff. So after class we will often have lengthy conversations comparing what we do to other things we have seen or experienced so we can better understand why we do what we do ...understanding that there may be no "best" way, just different approaches.
So if I had to share a studio with the WC guy down the street, I'd have to get him on board and maybe at some point do some joint workshops where we talk about similarities and differences. From my previous contacts with him, I'm pretty sure he'd be open to at least talking about the idea. Decent guy.
On the other hand, the association I first belonged to preached the
we're right and they're wrong line ...or more like
we're superior and they're all really stupid line. And even informal training with other groups was really frowned upon. Even among (or
especially among) people that had previously trained in our lineage and association. Very cult-ish.
So if you are in dealing with anyone like that, or anyone who is 100% about making money and crushing any possible competition, better walk the other way.
BTW if you give this a try, keep us posted and let us know how it works out.