Neighborhood Stories : Jealousy and Romantic Rivalry. For example Dina Caliente could become the rival of Bella Goth and try to seduce Mortimer, Bella would fight back. The player could decide to support one of them or stay out of this conflict.
Jealousy isn't about breaking up as quickly as possible, it's refusing to share with others and being possessive so the gameplay could focus on spying the partner and doing protective actions to keep others away (Jealous aura).
Romantic Rivalry isn't a new type of relationship, it's a goal to reach. Two friends could fight over a partner without damaging their friendship, it's competition.
Romantic Secrets : These secrets that could attract or repel any partner, they could be used to blackmail a rival (forced to break up) or be revealed to the partner with the risk to get an unexpected reaction (the partner could love the rival even more after that).

It could be an opportunity for humor, I mean what crazy things could the sims do for love ? Sabotage date (partner + rival) (Voodoo doll ???), spy partner, do something very romantic to gain the partner loyalty, train a cowplant to scare the rivals.