The King : Eternal Monarch (2020)

in KTEM ML goes to portal into parallel dimension of the same time era . FL goes back in time cause of a rock. but in both dramas the leads can go back and forth into their dimension/time. which is rare in dramas with time travel. mostly it shows one of the leads to be stuck in one time and never able to come back and how they settle there, many of the times in someone else's body. thats why i though this might be a good suggestion

Korean emperor Lee Gon tries to close the doors to a parallel world which was opened by demons; a detective tries to protect the people and the one she loves.

-concept of parallel world in both the shows
-crossing over to other world, lead actor takes the actress who actually doesn't believe in his words.
-secret of gateway to other world is known by few people and evil people come to covet it.

two different dimensions or different era. similar romance. mystery, humor and overall vibe is very similar. ( Chicago typewriter is less complicated than TKEM so if u dropped TKEM because of it complicated plot/story-line try Chicago typewriter)

During the Joseon Dynasty, a young woman named Hong Chun Ki is a painter – a true rarity in Joseon Korea, where Confucian values dictate that such pursuits are unsuitable for a woman. She was born blind but somehow managed to acquire a sense of vision. And now she has been accepted to the most prestigious art college in the land. One day, she meets Ha Ram, an astrologer whose fate is the polar opposite of her own: Although he was born sighted, he lost his vision in a childhood accident. Regardless, he is also in possession of an astounding talent that allows him to read the future by tracing the movement of the sky at night despite the fact that he is blind. The duo is sucked into the machinations of the royal court, particularly those involving two princes, the free-spirited Prince Yang Myung and the cruel, scheming Prince Joo Hyang – a man who longs to become the next Joseon king.

Quiet and gentle, Min Jae Yi is everything a good daughter of a prominent family should be. Engaged to the son of the Second State Councillor, Jae Yi knows that the only way to bring herself and her family honor is to accept her fate, which she does with grace and charm. Devoting herself to learning everything she needs to know to become a good wife and mother, Jae Yi dutifully prepares for the future. Sadly, destiny has other plans for her future. Four days before her wedding, Jae Yi’s family is murdered. With no one else to blame for the unexpected tragedy, Jae Yi soon finds herself the object of baseless and horrifying accusations. Blamed for the death of her family, Jae Yi might not have had much of a future at all, if fate hadn’t decided to intervene. Bringing the lonely crown prince, Lee Hwan into her life at just the right moment, Jae Yi is saved from a dismal fate, but her salvation comes at a price. Plagued by a mysterious curse, Lee Hwan agrees to help Jae Yi, but only if she agrees to help him break his curse in return. Unable to refuse such an offer, Jae Yi agrees to the prince’s terms, setting them both on an unexpected path toward love. But what chance does their love have of surviving when one of them is a former murder suspect and the other is a cursed prince?

The action, royalty, share of ancient era in time in the same space, love, and memory lost. The ML are strong personalities.

Historical (sort of) + romance

CR is a cdrama set in chinese republican era (early to mid 1900s)

TheKing the modern monarch concept set in present time

Very similar feeling watching both, stunning cinematography & visuals and a romance with an aristocratic charming leader (king /ring leader )

King eternal has the parallel dimension storyline, when I saw "Tomorrow I'll meet the yesterday you", this drama came to my mind. Both has fated love partner. In both the shows, They save eachother through the different time portals and parallel dimensions!

Both have the Modern Monarchy concept + Romance with a king/prince

The main difference is TheKing drama has also timetravel & alternative realities fantasy element too, Goong has no fantasy element

I recommend this both drama because , Male lead and Female lead
try to solve problem
In one drama explosion and another student murder/suicide

-Both explore different time-lines (Kairos does it a little bit better)
- They both have a well developed Female Bad Guy (although the main Big Bad is a Guy)
- Both have a everyday FML, that takes action and is brave
- FML with a best friend that is in love with them

Kairos is a little darker (no humor and the only love story is between the bad guys), but it is very exciting and well written .

1) Both dramas involve time travel & parallel worlds (In Alice the time travel is explained scientifically whereas in The King it is more of a fantasy)
2) Both have romance & destiny elements
3) Both of them have police involved in time travel
4) Both the main leads seek revenge for their parents death
5) Both of them have good visual effects

Vanishing Time: A Boy Who Returned, has similar aspects to The King: Eternal Monarch, these aspects are:
-At a certain point the ML is stuck inside a world where time is frozen, and in both stories the MLs are the only ones who still go through time.
-in both stories, the ML is going through this time, in hopes of seeing the FL again.

Both series have multiverse concept. Just as 609 in The King the leads meet by traveling to parallel worlds