For either CC or weekly competitions.
This game format is a better ball 3-ball.
You and 2 friends enter competition and play stroke play.
Slightly longer play time than AS ( approx 1.5).
The lowest score on each hole goes on the card.
Winning team has the lowest score.
My old (real) golf club used to do this as a family day (Male/Lady/Junior).
It was always popular and a great social event.
You could make it that each player had to be in a different tier to encourage cross tier play. No player can re-enter same comp, so I'd make it a single play only format.
Sometimes of course, the pro of the group carries the other two, but at least the less good gollfer got to play with and learn from his betters, and was further encouraged by the kudos of finishing well in a competition.
Just a thought.
Regards
Martin