Euclid-Style

Parallel dating is a concept with which I was totally unfamiliar until relatively recently, but it seems there are social circles in which casually dating multiple people at the same time is acceptable and, indeed, universal.  (It is, of course, not so in all circles.)  Now, assuming traditional gender roles at least in the early stages of dating, this seems a lot more intuitive for women than for men: if you are generally in the position of being asked, declining just because you’ve been asked by someone else seems unnecessarily restrictive and, indeed, a practice that denies you of agency even more than the traditional gender roles do already.  If you are generally in the position of asking, however, the situation seems significantly more complicated.  If a man has gone on a couple dates with a woman but they haven’t yet figured out if they want to become more serious, and then he meets another woman, is it acceptable for him to ask the second woman out?  In circles that frown on parallel dating the answer would presumably be “no” until he knows what he’s doing with the first woman, but how does this work if parallel dating is the norm?