can you have 2 girlfriends??
As JaSteel said, you can add to your harem every girls in the game, but you'll have to be a little cautious if you want to avoid break up.
I recommend talking about it with your first girlfriend (Talk with her > Relationship status > I wanted to ask about [Another girl]). This conversation becomes unavoidable when the Love stat of the new girl reaches 800.
Or you may forget the lovey-dovey stuff, level up the Love stat just what is needed to have your fun with the girl and enjoy the ride. This way, no strings attached, no headache.
But since you asked about
girlfriends, I presumed you wanted to know how to drag them in the long run...