I'm looking for something with multiple story lines, however not in form of there being a main couple and a supporting couple. I would like if all the characters involved are the main couple, for an example something like Better Man, where the three brothers have their own romance story, or Dear Mom, where the four sisters also get their own story line.

The Gentlemen of Wolgyesu Tailor Shop
I haven't seen it yet but it's in my plan to watch: The Lover
And maybe Fantastic or Age of Youth
There is also Reply 1988 which revolves around the whole neighborhood but it's not only romance related
Age of youth
Reply 1988
Fight for my way
a gentleman's dignity
plus nine boys
Oh my venus
Basically every KBS weekender like: Ojakgyo Brothers, Unexpected You, You're The Best Lee Soon Shin, Five Enough, All About My Mom.

A few more: Glorious Day and Dear Mom (taiwanese)
Ode to joy season 01 & 02.
+++ Ojakgyo brothers ; A Gentleman's Dignity

Ugly Alert
high society
Brother beat/my prince
A Gentleman's Dignity
The Lover
I Need Romance 3
Father is strange, Father is strange, Father is strange
Definitely check out Love Shuffle! It focuses on 8 characters who swap relationships so there are multiple romance storylines!
Love shuffle
Tokyo tarareba musume
QUARTET
It has a best script and solid cast 
thanks, ill check out all of them :)
Reply 1988
Descendants of the Sun
Goblin
Fight for my Way