It's open-ended!
1. The finale episode was written and edited in a way that it can serve as the series finale.
2. With the final scene as a possible window into Season 04 if they get an order for it / or green light.
But, you see, Season 04 is going to be a big challenge for them:
a. Growing number of characters - they will need a huge budget for that.
b. Let's face it, Eun Tak and Ah Reum's story doesn't make any sense. It turns from this direction and changes again, just like that.
A sure sign they are trying to fit in too many stories.
c. There's Doldam and the Trauma Center. It's going to be very challenging to pull that off.
And Season 03 is kind of an experiment if they can do it. But as you can see… they almost failed.
d. There are other characters that haven't returned. Some of them were shown in the last episode. THE FAMILY is not yet complete. (Here we go again with “The Family”.)
There are only two possible ways they go forward with this:
1. This is the series finale for Dr. Romantic. It's time to split it into two spin-offs. The Doldam Hospital part and the Trauma Center part.
I've seen a series, decades ago, who did this. Two spin-offs that are actually very close to each other. Basically, all they have to do is focus the episodes on one area only.
They can even have fun with this setup. With occasional guest appearances. Or, we'll get updates through dialogues.
The most fun they can do is, we have to watch both spin-offs to see the bigger picture. The bigger plot. The major arc story.
Doldam spin-off is 10–12 episodes.
Trauma Center spin-off is 10–12 episodes.
Here's yet more fun.
2 episodes of Doldam Monday and Tuesday schedule.
2 episodes of Trauma Center every Thursday and Friday.
These episodes are happening close to each other as far as time line is concerned.
2. If they will not create spin-offs, they have to reduce the cast, which is a very risky decision because fans will not like it.
However, again, no spin-off = some casts has to go. They can be guests, but that's it.
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A spin-off is possible because we have a new antagonist, the assemblywoman.
Also, the National Ministry for Health also challenged the Trauma Center to stick to the requirements to only use the provided machines and supplies for trauma patients, otherwise, they'll have to ask for permission again.
You see, basically, the story of “Dr. Romantic” is done. Master Kim's students learned what they need, and can now stand on their own. They are ready to handle the Trauma Center by themselves.
Master Kim and Director Park are there as behind-the-scenes support. And Director Park showing up at Doldam is itself a sign that the Trauma Center was left for the next generation.
With the “Romantic” arc done, it makes no sense to have a Season 4.
Instead, to spin-off series fits well. They can also have the freedom to write a new plot without making Master Kim the center character.
Because, like it or not, “Dr. Romantic” is about Master Kim. His method of teaching. The things he learned himself and passing on to the new generation, and so on and so forth.
Again, that's over.
Writing a new plot while retaining the title and Master Kim would only result in disappointments because people already have expectations.
However, if you split it into two spin-offs, there won't be any expectations. And Master Kim doesn't have to be the “glue” keeping them apart.
Lastly, Season 4 doesn't make sense because it will mean all of them will still be under Master Kim's shadows. The ending of the Episode 16 did not give us that… they all “graduated” already, and the Trauma Center is theirs to manage.