I personally wouldn’t date 2 girls at the same time (be officially committed to 2 girls at once), and if I found out that a girl I was dating was dating a dif guy at the same time, I would “dump” her. The excuse that some people have to compare dates, is not a persuasive one. If you need to compare guys/girls, just compare the guy or girl to the previous guys/girls he/she dated in the past. I do not understand why when comparing guys/girls it has to be between guys/girls who one is dating at the same time?!? That said, in my yeshiva 2 guys were officially dating the same girl at the same time, and they both found out about it, weren’t happy about it, and both dumped her at the same time! Although, it is only one story, and i’m sure there are others out there, where the guys/girls involved did not care, I would say most guys would not be happy if they found out the girl they were dating was also dating a dif. guy the same time.
On the other hand, once one side ends a shidduch, I believe both the guy and girl can look to date someone else right away, if they are ready. Therefore, there should be no problem with someone dating 2 people on the same day, as long as he/she is no longer going out with the first date.