What Kanai's Cube recipes are not listed?
There is a help section in the Kanai's Cube tab that shows 7 pages of different recipes.
I know that you can also put in a Puzzle Ring and that will open a portal to The Vault.
Are there others?
As you have said, you are able to place a Puzzle Ring inside Kanai's cube, hit transmute and a portal to the Treasure Realm will be opened. Likewise if you place a Bovine Bardiche, a legendary Polearm, in the cube and hit transmute, a portal that definitely doesn't lead to a secret cow level, definitely won't open, wink. These are the only currently known secret cube recipes.