Untitled Tuesday - not a league, but a live tournament: https://www.chess.com/club/untitled-tuesday
Not-so Pro Chess League - like the Pro Chess League, but not so pro: https://www.chess.com/club/not-so-pro-chess-league
Club Chess Tour - not a league, but a series of team match tournaments; https://www.chess.com/club/club-chess-tour
Team Match Championship League - like World League, but for teams that don't have a regional/national affiliation: https://www.chess.com/club/team-match-championship-league
It's A Knockout Vote Chess - vote chess tournaments: https://www.chess.com/club/its-a-knockout-vote-chess
It's A Knockout - team match tournament: https://www.chess.com/club/it-s-a-knockout
I'm sure there are others.
Is there a list of all the active Chess.com League competitions?
I am aware of Countries of the World League, World Cities League, and a Space League. Are there more?