Do 6-, 10- or even 20-pole rotary switches exist for 220V applications?
What you want is called a "cam switch", but I don't know of anyone who makes one with more than 12 positions as a standard product off the shelf. But one of the larger mfrs in the world who brand-labels to most of the other electrical equipment suppliers is Kraus Naimer, and they will make you anything you want, up to 24 positions. Understand though that once you get above about 12 positions, the rotating distance between each step becomes too low for larger contacts, so at 20 positions you may limit yourself to microswitch contacts, so 1 or 2 amps of capacity. Bot for LEDs, that should be OK.

Another mfr is Electroswitch, but at that many positions I think it will be "military" grade and very expensive.