In Persona 5, you're able to date 9 different girls. However, after choosing to date one, the option still comes up for others. If I choose to date another, are there any consequences?
Similar to Persona 4 (but amplified due to more available women), everything will go just fine until Valentine's Day. After choosing to spend time with a girl, the others will all show up the next day, beat you up, then dump you.
The most extreme case of this can be seen in this video, where the player is confronted by the 8 women he ignored on Valentine's Day.
This has no bearing on the plot or your Social Links in that playthrough and you'll still keep the chocolate from the girl you chose to spend time with on Valentine's Day, as mentioned by a couple people in this thread:
You don't lose your max confidant items [...] You keep all Christmas and Valentines gifts you received into NG+ regardless of cheating.
In fact, you actually end up with an extra (pity) chocolate from Sojiro, according to a post here:
you still get chocolate from the girl you picked for Valentine's day and pity chocolate from Sojiro.
Thus, if you choose to cheat, you actually receive more than if you'd stayed faithful.