It may be possible, I'm not aware on any upper limit of Vives you can run in one room, but there will inevitably be EM crosstalk/interference eventually no matter what you do. The important thing to remember is that you can and should run multiple Vives on a SINGLE pair of base stations. More than two base stations in a single playspace will not work properly.
"Welcome to the desert of the real."
If your base station has a Fault 02/03 error or a red light or both, the ONLY solution is to contact our support on vive.com and set up an RMA. There is no user fix for this issue.
Also remember, with so people moving around it's important to have good cable management to ensure safety. Like @Synthesis said, you can only use two basestations per tracked volume (but can use multiple headsets in a single tracked volume).You'll need to isolate basestation pairs/tracked volumes from one another using walls or barriers that are opaque to 850nm infrared light.
To reach Viveport's customer service team, email email@example.com David R
Technical Specialist - San Francisco, CA; Monday-Friday