Dramas where at least three guys fall for the FL at some point (to the point of wanting to marry her and / or being willing to die for her):
- Imperial Doctress
- The King's Woman
- Moon Lovers: Scarlet Heart Ryeo
Dramas where at least two guys are romantically interested in the FL (and in most cases she is surrounded by men / has support from other male characters):
Chinese historical, fantasy, or fusion dramas:
- The Princess Wei Young
- Sound of the Desert
- Princess Agents (warning - it ends in a cliffhanger)
- Lost Love in Times
- Love O2O
Korean gender-bender dramas:
- Love in the Moonlight
- Sungkyunkwan Scandal
- Coffee Prince
- You're Beautiful
- To the Beautiful You
- Empress Ki (the gender bender part is short lived)
Other Korean genres (the "everyone loves her" factor isn't as strong in some of these):
- I Remember You / Hello Monster (crime drama - the romance is not as front-and-center in this one)
- Pinocchio (romcom / thriller / mystery)
- She Was Pretty (romcom - the SMLS is strong with this one)
- I Hear Your Voice (noona romance / law / supernatural)
- Dream High (high school / music - warning the FL is hard to like)
- Sassy Go Go (high school / dance)
- Marriage Contract (fake marriage / terminal illness)
- The King in Love (historical)
- Hwarang (historical)
- Live Up to Your Name (medical / time travel)
- Doctors (medical)
- Witch's Romance (noona / reverse workplace)
My favourites are in bold. Sorry for repeating some from your list / from the suggestions above.