If there are several game modes
available from the start, we allow every such mode to be published in Vault, counting each of them as vaultable any%. It's also possible to have a movie that beats all such modes in one go.
http://tasvideos.org/MovieRules.html#GamesWithAdditionalLevelSetsOrGames
If there are optional characters available in the game (not necessarily from the start), we only allow the fastest one to be published in Vault as an any% branch.
http://tasvideos.org/MovieClassGuidelines.html#UsesASuboptimalCharacter
The question is, how do we distinguish between them?
If we have several chars from the start, and they play the same levels, but bosses differ, is it a secondary game mode?
If some chars can access route deviations while the game otherwise remains the same, is it a secondary game mode? What if just a few levels are different?
If the first release of the game had a char as a DLC, and then it was included and became available from the start, though it plays through the same levels, is it a secondary game mode?
In S3&K, Knuckles plays different levels than Sonic, so he can arguably be called a special game mode.
In Shovel Knight, the Plague character was a DLC, and then was included in the game. His movie is shorter. He plays the same levels as Shovel Knight. I would not dare to call Shovel Knight a suboptimal character for that game...