Speaking as someone who has 3 male leads for the 1 female protagonist, I don't mind them if done well. 
I think the main thing to keep in mind is to not fall into the jealousy trap. It's a bit easy and overdone, hence why so many people groan about it.
For example, one of my male leads is pretty jealous but that's because he's a monster and doesn't go by human customs. He also has a particularly vested interest in preserving the connection he has with the protagonist because he needs her to live.
For the other two men, they don't really see each other as rivals. In fact, they only ever have a brief encounter with each other. One is mostly interested in his own business while the other is only concerned because the protagonist hasn't really ventured away from her home to fraternize with strangers before and is worried about her safety.
Also if the second guy is thrown in just to cause drama, but it's obvious the lead will end up with the first one anyway, is another thing I've heard people rolling their eyes at.
In my story the protagonist could feasibly end up with any of them and spoilers she ends up with 2 of them!
Third, each love interest should have their own lives separate from their relationship to the lead. Otherwise it leads to flat characters that only exist for the sake of being a love interest, which is another gripe I hear.
Granted, my monster character isn't very physically separate from the protagonist, but he retains his own motivations and desires and he isn't all about "winning the girl". He mostly wants to survive and maintain what he thinks he owns.
Anyway, hope this helps!