I was watching Boku no ita Jikann and the male lead's friend tries to steal his girlfriend (female lead) pretty early on. Anything like that? Maybe the female lead wavers a bit because how the friend goes about it and that causes problems for lead's relationship.
I think with some of these the SML may have showed his interest first and the ML then wants the girl afterwards. Or the ML didn't want the girl until the SML started moving in.