You can be a member of more than one team, but you need to just make one of those teams your "primary" team. I'm not sure if you can enter two events at the same time with different teams though (if that's what you're asking?). I presume whatever team you have set as your primary team will be your team for any events you join - but I haven't tested that
You can ride for 2 different teams in 2 Leagues in the same period.
I'm riding for WTRL in TTT and iTT but Cyclechat in the DBR league. You're right that you can flip your team as you said above. That's what I was doing until this week. But after the DBR race on Monday, I flipped back to WTRL and about 10 minutes later I was showing as a WTRL rider in the DBR event, so I had to flip back to make sure my result was processed by Zwiftpwower as a CC rider and not as a WTRL rider..
Then I found this way to fix it, but it's obscure and I was just lucky to stumble across it. So, what I've done is set WTRL as my Primary Team. Obviously, that means if I enter any leagues or races I'll ride as a WTRL rider. But, if I go to Zwiftpower, click on Leagues on the top menu bar, choose DBR Wahoo League from the drop down menu, click on Events on the next page that gives a list of events that have taken place. Tap on any of them and you get the results for that event, but on the menu bar at the right hand side there is an option called Settings. Click on that and a box pops up in the bottom left hand corner with 2 choices for your team and your name. So by default my team for DBR was set to my Primary Team. But when I clicked inside the team box I got another drop down menu which lists all my teams. I used this to select Cyclechat which means that only for the DBR league my team is now Cyclechat and not my default team. This setting only affects the league you apply it to. Your Primary Team is unchanged.
So, if
@Brendan Parker wants his default team to remain as Cyclechat but to ride for BRT in the 3R league all he has to do is rejoin Cyclechat, make CC his Primary Team, then go to the Events page in the 3R league, choose this weeks race, then click on Settings and change his Team for the 3R event to BRT. Hey presto! Done. He's now a CC rider, but he rides for BRT in the 3R league. Obviously, he could do all this in reverse and make BRT his Primary Team and then choose to ride for CC in a league if he chooses to. That's what I'm doing right now.
Interestingly, you can also change your name for an individual league, except I've no idea why you would want to do that......... although I suppose you could have a bit of fun with that option.