Rather than your typical love triangle or quad or whatever, we have ships or couples who are rivals. 

OK, so I take it that you want a secondary couple who are rivals with the main couple to be the absolute power-couple? Like Jay-Beyonce VS Kim-Kanye or Benifer VS Brangelina? 

So, I searched through my watchlist and I found a few, but there's always an element of love triangle at some point or another (like a person from couple B being either the ex or having feelings for a person from couple A). But in all these dramas the rivalry has nothing to do with the love triangle, it's more coincidence.

Ab Ruk Online the women are rivals at work.

Cruel Romance there's a strong rivalry between the two women and also between the two men, and at some point there's  (unnecessary) love triangle happening. 

Game Sanaeha The FL is a rival to another woman for personal reasons. There's a light element of love triangle.

Halik this one has a huge love square, because both main characters lose their spouse to the other's spouse. But I still put it in here because the work/money rivalry is pretty intense.

Lying Heart this is another love triangle but the secondary couple works pretty hard together against the main couple.

Moonshine and Valentine This is about a rival ship. There's a strong love triangle, but with a little twist (the 2 FL is a good person)

Pleng Bin Bai Ngiw The two leads have to contend with their spouses joining hands against them.

So Wayree This has no real love triangle, the ML has a jealous 'cousin' who has a relationship with the FL's jealous friend.

The Love Proposal still airing, the bad guy and his mom (yeah I know it's weird but she's a milf and they look good together) are the rivals to his cousin and the FL.

Secret there's a weird love triangle, but the bad couple really work hard to ruin the FL's life.