Technically speaking, right now there are only 2 classes as far as the game is concerned: frigates and capitals. The game treats cruisers the same as frigates, they just have their own tab in the frigate factory.
But no, you can't add more. Any ship has to be either a frigate (and can go into either of the 2 build pages on the frigate factory) or a capital (that can only go into the capital factory build list).
This is excluding the fighter types, of course 