Not yet. It might also not be possible to
technically make all of them your girlfriends when the game is done, particularly for the fey creatures. I'm doing whatever feels natural for each of the girls instead of trying to fit them all into the same square hole.
Each of them will have some kind of romantic climax (both meanings of the word apply) though, even if they're not technically your girlfriend afterward. Romance is also not the only possible result of your interactions with them, and in a few cases might even be detrimental to your eventual success. It'll all make sense eventually, trust me.
In the current version of the game, the following girls can be your girlfriends, though more are possible to romance: