Recommendations

While male/female roles are reversed from Secretary Kim , Encounter also features a romance between an employee and the top executive of the company. The backdrops of both dramas feature filial piety and the chaos that brings with it which creates drama that that makes for excellent story lines. In both there is secrecy and chaos. Both feature the relationships as central theme of the drama. Both dramas are wonderfully written and have excellent OSTs as well!

School 2013 is about friendships and general school life. It's about grades and keeping up with school and life. Not really in the crime drama trope, it has similar themes of friendship and cooperation.

Similar themes of school students in really strange situations. Watch with the lights on, though. THIRteen Terrors is not the teen centric lovey dovey teen drama, but a collection of some really scary, goose bump inducing, cringe worthy stories.

Similar themes of school based crime, school life, teachers, greed for power and mostly the same actors.

Both involve kidnappings of already engaged women, both FLs not in love with their fiance. However, the kidnapping is later in Hua Jai Teuan. Suparburoot has more skinship and flirting, and Hua Jai has more revenge. Both have MLs separated from their families with some level of mystery about their heritage.

In both productions a bunch of dirty cops, riffraffs and prosecutors use unconventional methods to take down powerful and corrupted politicians. Both have lots of violence, although Asura is slightly bloodier.

An immortal waits for centuries for a maiden to break a curse that prevents him from moving on. Even the promo art is reflective of each other.

Both male main characters have an illness that makes it difficult to be a doctor but both pursue to be doctors and do their best despite their weaknesses.
Both dramas have romance between doctors and residents. It's not the main focus of either story.
Medical mysteries do not overwhelm the story with things to do so that there is no more room for character development. Characters build a strong relationship with each other and with themselves.

Autumn Tale isn't a period drama, but there are similarities:

Both are beautiful, heartbreaking love stories. I cried the most watching these two love triangles (or other rectangular). Both are tragedies.

Both shows are socially tragic and both depict the struggles that occur in the upper echelons of Korean society. Furthermore,both shows feature leads who are loyal dogs to the upper class though not high class themselves but have the know how to bring down their glass houses

In both these sageuk, the crown princess/queen selection is a focal point of the intrigue.
The crown prince/king prince influences on the selection process because he's already smitten.

They both have the cinderella type of story when it comes to their female leads.
story both includes a grim reaper.
you'll cry so much on the ending.
age gaps on male & female leads

It is the sequel to the first season so it's the same setup and with a few of the same players, so if you liked the first season you might like the second.

Both characters are sent to a place that deals with animals that they aren't familiar with. Both leads end up liking farming and make good friendship along the way.

They are both about catching bad guys in bad guys technique.
The main leads are in both shows are parents who lose their kids due to the unjust people of this world.
There are hackers and fighting experts.