From top down, order of recommendation:
Life. Has really well rounded characters, but not a lot of individual cases, as the main focus was the politics. Watching this ruined hospital politics in any other drama for me, so I recommend trying it, it's on a whole other level. Also from one of my favourite screenwriters, anyone will love it if they love the genre. Multiple main leads.
Hospital Playlist. Currently airing, could very well usurp Life as my favourite medical drama. Also from some very trusted screenwriters. Multiple main leads. EDIT: Woops you said I didn't need to rec this, oh well.
Kounodori. Hands down, my favourite Jdrama. Also my favourite medical Jdrama by default, this is full of beautiful human stories about life (and sometimes death). Only a Jdrama can achieve this.
Cross. Starts in a prison, but later on it's mostly in a hospital. Great revenge and redemption story. It focuses on organ transplants and really only follows one doctor on his journey, although there's some great side characters.
Dr John. Not the best, but not the worst, although I can't say how accurate it is in its information. Again, it starts in a prison, but shifts to a hospital setting. It's also a romance, but I watched it because of the actors and it was decent (the politics weren't too bad).
D-Day. I dropped it, but you may be interested. It's a what-if for an extreme earth-quake in Seoul and the aftermath, from the perspective of the doctors. It could have been very good without the intrusive and unnecessary hospital politics, but you may be able to overlook that.
Heart Surgeons. So far I've only seen the first episode, but it's on my PTW list. Looks like what you want, although I can't really judge how good it is.
Good Doctor. There's choices, it's been adapted in many countries, but the Kdrama is the original. There's also a Jdrama version. It's about a doctor with Savant syndrome, but I was very irritated with the Kdrama vers, as there was some misinformation. Anyway, it's about someone wanting to save lives, but the politics may annoy you.
A Poem a Day. It's set in a hospital, but not about doctors. It's about the people who work there but are not doctors. I haven't seen it, but it's on my PTW list and others say it is good.
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Everything except Kounodori is a Kdrama. I hope there's something in there for you.