There aren't really "consequences", per se, it's not like one or more of the girls isw going to react negatively to you being a man-whore, but you do have to choose between going with Georgina or Jennifer as currently (and hopefully just for now, we'll see what the rework brings) you can't have both of them. But you can seemingly pursue Georgina and and Elena at the same time, or Elena and Jennifer at the same time, and these will eventually merge into a D+E+J path, or a D+G path and a D+E path.
I'm still holding out hope we can get a D+E+J+G path, but we'll have to see if this rework they're doing on the chapters will allow for that as it would be the best ending, in my opinion.
Also, you can do things with Margo and Olivia, but that will open up sharing routes with their respective partners, Ryan and Graham.