Not far down the page is my thread on Variant civs - there’s probably no need for a duplicate!
Anyway, the main conclusion is that Variants have no place in AOE3 and the Home City system pretty much allows you to make ‘your own’ variant anyway. Then you also have the Revolutions which are a variant type, though after investment in your current civ.
Obviously it would be lovely later on to have shipments that could fundamentally change certain parts of your civ (I always bring in a Scottish Covenanter/Jacobite offshoot here!) but we’re nearly there with some of the HC cards, like Elector Princes for Germany.