Is multiple live games at once allowed by lichess or not?

Recently I found out that it was possible to play multiple boards, and I was happy because it is a chance for me to play longer time controls without being bored. But I noticed that sometimes lichess allows me to do it, sometimes it says "You have a game in progress with playerX, you can't start a new game until this one is finished". I'm getting mixed signals... is lichess being passive/aggressive? :/

What is the official policy about this?

I can't speak for the official policy but I've noticed the following for my (bot) account (and I believe it's the same for non-bots):
1. You can start new games as long as it isn't your turn to move for each and every ongoing game
2. You can offer a rematch and/or accept challenges regardless of whether you're playing any games or not

@LeelaWeak It seems you are right! Thanks!