Girls you get to do stuff with is 4 [as of ep. 5] if I'm not forgetting any, but there's a lot of suggestion for I think 3 others. It's good content with a good story.
Edit: I forgot Grandma, but I don't count her cause ewwwwwww...
Whaaaat? I count twenty-two named female characters so far (nineteen are listed in the phone contacts, with sixteen of them showing a stat of whether or not you are on their "route"), and by the end of ep5 you've done stuff with almost half of them. Story threads are there for the rest of them as well - I think you'll probably have the opportunity to do stuff with almost all of them before the story is over.