I'm not huge on chaebols, but one drama I do like quite a bit is shopping king louie. I also suggest mask, my name is kim sam soon, protect the boss, & fated to love you. I dropped FTLY but it is a very popular drama regardless, as is mask (which I had to put on hold). cheese in the trap is an interesting drama, even tho I don't particularly like the end & stopped enjoying it around ep 12. unless I remember incorrectly, I think me too, flower! falls under the chaebol drama category. the leads are cute together but the drama itself is nothing to rave about, yet I still enjoyed marathoning it.
others would be...
boys over flowers (I will never rewatch this but it is a popular pick)
heirs (by secret garden writer kim eun sook. I felt super bored with this)
falling for innocence (felt it was a lukewarm, tropey melo but watchable, kind of addicting)
beautiful gong shim (good start but the focus shift from fmc to mmc greatly disappointed me & the ending fell flat IMO)
goong (I watched this for the young YEH, but I wouldn't sit through it again lol...)
flower boy ramyun shop (no opinion/dropped after ep 2)
cheongdamdong alice (got draggy; dropped)
^^^ I don't personally rec what I didn't bold but you never know what someone else's preferences are. master's sun is another popular one that lots of people seem to enjoy, but I have yet to watch it.
I hope you find something to enjoy (: