Lost Romance: fabulous and fun. It also has some kDrama shoutouts.

I wouldn't call it a K-drama, but Viki's original series Dramaworld has an American girl sucked into a K-drama.

In Kdramas, EY and W are the only ones I know, I think.

Memories of Alhambra is the ML stuck half in a video game and half in the reality.

If you're open to webcomics, I have a MILLION suggestions, lol. "Modern Korean girl dies and wakes up in her favorite fantasy novel" is a hugely popular genre. I imagine someday at least a few of them will get adapted into dramas.

The list is likely to be short for dramas.

One drama I can suggest is W four worlds.
Only, it's not filmed, it's a visual screenplay. The closest rendering to TV.
- It's the unofficial season 2 of W two worlds, as if it were the real thing. With a crazy new plot, the extension of the high-concept with logic, plot-twists, emotional rollercoasters, in short, the same spirit as season 1. You feel at home.
- With characters from the original drama. And for the new characters, since the format use photos, actors Lee Jong Gi, Kim So Hyun and Kim Tae Hee.
- It's more easy to read than anything. Even books for children.
- Links to the screenplay are on my Wall page here.
Click on my profile.
@jenzy might be interested? I created it for people who love W and myself, and even imagining that the story might surprise W's screenwriter.

Other proposals, but not just books:
- The kdrama "dramaworld": proposes a heroine who enters the world of dramas.
- The US movie "Last Action Hero": proposes a child who enters an action movie.
- The US movie "The Never-Ending Story": features a child who enters the world of a fantasy book.
There are undoubtedly others, older films, Japanese anime...

Alice's Adventures in Wonderland as told by Lewis Carroll and illustrated by John Tenniel? Quite creepy on any number of levels!

I recently watched C-Drama The Romance of Tiger and Rose, which was a light and fluffy take on this concept.

And I've been waiting (and waiting and waiting) for Netflix to release Queen of the Scene with Gong Hyo Jin as a makjang writer suddenly trapped in one of her stories.

About crossing the line between two worlds, here is some clarification:

"Breaking the 3rd wall" is when the actors are aware that the characters are in a production (when leads fall in love and say "This is like the perfect ending of a RomCom.")

"Breaking the 4th wall" is when characters respond directly to the audience (the real world--when Peter Pan asks the audience to save Tinkerbell).

I'm not sure about the alternate worlds storyline setup, but does "King: Eternal Monarch" count?

A pair of recent C-dramas:
To Ship Someone — Optimistic editor gets sucked into novel along with its pessimistic author.
Catch Up My Prince — Medical intern winds up in role-playing video game and must complete quests if she hopes to escape back to reality.

Chinese Webdrama My Supervisor Husband had so much fun with this concept, it was short but very nice. Night of Love With You is another webdrama on a very similar theme.

You can't go wrong with the previously mentioned Lost Romance as well. It has the most wonderful SML so beware of second lead syndrome.

Lost Romance is the Taiwanese drama in which female lead gets sucked into overbearing CEO novel. It’s quite fun.
Romance of the Tiger and the Rose is the C-drama where writer is transported into her crappy drama script. The meta elements in her show within the show are quite funny. One example – male lead is for female lead but second male lead is for everyone else.
In Joy of life male lead writes a novel in which a modern man transports back into ancient time. It was done so get past the sensors.

I'm fascinated by how few K-dramas incorporate this concept, especially with so many time travel/time twist/past life dramas... this storyline seems like a natural fit.

Tangential to the topic- I wonder if Isekai (a genre very similar to this if not this exactly) will become the next big thing in dramaland? There is, at least, a plethora of source webtoons, novels etc. For adaptation dramas (continuing in the thread of adaptations). It's a pretty big genre.

Extraordinary You is by far the best example of this genre, although I tend to think W: Two Worlds is better than it gets credit for (albeit entirely by accident, judging from the trainwreck nature of the writer's filmography).

Extraordinary You is the only one that pokes gentle fun at Kdrama tropes, critiques bad writing, is a great little story and also deals properly with its metaphysics. It's quite a masterpiece considering there's no 'outside' world for the fictional world to intersect with and I genuinely thought it would collapse because of it.

Sucked literally into a fictional world?
W Two Worlds
Memories of the Alhambra

Characters adventuring in a different dimension? That's a bit easier:
Train
The Heavenly Idol
Welcome2Life
King: the Eternal Monarch

Tangential Mention: Daily Dose of Sunshine, for the one character who thinks they live inside the game even though they don't.

I feel like this is more common in c drama than in kdrama? I had a look on my drama list with the tag “fictional world” and apart from Extraordinary You and W, it’s basically all cdrama.

An English example might be Lost in Austen? She gets sucked into Pride and Prejudice (changes places with Elizabeth Bennet?) and then tries to keep the story on track but it goes off the rails. I barely remember it so I can’t say if it’s any good or not 😅

I really can't recommend any cause I'm watching my first of that genre, right now...
ON THAT NOTE, what excellent timing! I've never been able to engage in these Beanie Recs with any fresh input but I can talk a little right now. If someone was to suggest a 'sucked into an alternative world', I would ask if the 3 timelines compliment or contrast each other.
"What are the 3 timelines?", you ask.
1. The Real World Timeline
2. The Alternative World Timeline
and 3. The Cinematic Timeline.
I'm compiling notes and illustrations on how 'W: Two Worlds Apart' does not have complimentary timelines and how much it bothers me. We'll see how I feel when I finish.

How about Galaxy Quest? Though it's a little opposite of everything, but still; the fictive becomes real.
https://giphy.com/gifs/3ohzdNPJYCV4CHIneM