I need Romance 2
I need Romance 3

In both of these, the female lead gains feelings for both the male lead and 2nd guy. She then is conflicted because of it before choosing one.
Scarlet Heart Ryeo
Empress Ki
Missing You
The Heirs
All the flower boy dramas....
What Happened in Bali
All three are Novels by same author ... notice a theme?..... .... SotD and BBJX have same producer, director, screen writer and lead actress.  
Sound of the Desert 
--- Intense and very good.... She loves one, later another, both remain dear to her.
Best Time  --- Her obsession w/ her first love is stupid and annoying, but Lead guy is perfect!
Scarlet Heart / Bu Bu Jing Xin --- Loves first guy, later leaves him and hooks up w/  lead guy..... Excellent writing!

Also:
Summer's desire --- back and forth b/w the two until the end, when she finally makes a decision.
Love of the Agean Sea --- heavy triangle
Too Late to Say I Love You ---- the triangle or square is strong, but no matter what, the leads only love each other.
Empress Ki --- She loves one, eventually the other
East of Eden ---  Laden w/ all sorts of triangle, romantic ones, familial or bromance-type ... All relationships come in 3's... Excellent writing, good characters.


Not really heavy, but good:
9 End 2 Out ---- She dates one and befriends the other... things change.
Summer's desire
Goong
Que Sera, Sera
Hi 

Am going to keep an eye on this, as I also quite like triangles. 

As s.b. above already suggested, the I need Romance series all included strong triangles, number 1 as well.

I can also recommend

Beloved
Fated to Love You
Queen Seon Deok
Jealousy Incarnate
Strawberry on the Shortcake
Last Cinderella
When a man is in love
In Time with You
Discovery of Romance.

Enjoy
The Reply Series is pretty infamous with this trope.