If you want more on the investigation cop/ prosecutor genre try Stranger . It has two seasons so it'll keep you entertained for a while. This has a solid cast with great writing and you'll definitely be racking your brains trying to figure out who done it.
Another murder mystery but with comedy is Psychopath diary. This might take an episode or two to really get going but stick with it and you'll enjoy it.
Another one I like is a contract marriage drama calledFated to love you. There are many versions of this, Taiwanese being the original. I have watched the Korean version. This is either a hit or a miss. The leads are amazing actors and the Ost fits the story perfectly. Fyi, if you start this and get thrown off by his laugh (welcome to the club) stick with it, it really grows on you. Please don't judge this drama based on the first episode only.
A back to the past romance drama: Go back couple. A divorced couple get sent back to their high school years where they rediscover their youth and heal eachother's wounds.
A must watch history drama: Mr. Queen . Great comedy, acting,story. 9.0 rating
Redemption genre: Welcome 2 life . An immoral lawyer get sent to a parallel universe where he has a family and strived to be a decent human being.
Similar concept of parallel universe in Train. A cop boards a train to a parallel universe to catch a serial killer.
Hope this helps! :)