Sounds like you might be looking for ensemble cast/multiple mains types of productions? Also, multiple couples dramas?
Korea tends to do more with this style than other countries:
- Search WWW
- Be Melodramatic
- Hospital Playlist
- Korean Odyssey (no multiple couples though)
- Cafe Minamdang
Here are some other ones though:
- Rose in Da House (no romance)
- The Lost Tomb franchise (no romance)
- 17.3 About Love
- Shujin-ko
There's also episodic and anthology dramas, where each episode may focus on different characters in the storyworld:
- The Leaked (no solid romance line though)
- One Night Morning
- Midnight Diner
Older dramas, especially dealing with teens, also did this quite a bit:
- Kiss
Or are you more looking for dramas where there can be distinct leads, but theyre just average everyday folks and the only thing special about them is that the story is focused on them with a lot of the screentime?