I've done both karate and taekwondo and I would recommend the latter for jumping kicks. Karate practitioners don't do too many jumping kicks and the pace of taekwondo will definitely give you diversity and mobility. A great addition to boxing or muay thai foundations. I did martial arts first and boxing after and I was a beast competition wise. After adding mobility and footwork to your base skills, you can pick up most anything afterwards. I was kickboxing as an amateur for a while with positive results. So that's my opinion.

"Karate" isn't a martial art. It's a general term to describe martial arts from Okinawa and Japan.

TKD is a very popular Korean martial art that has become more sport than martial (or combat).

My suggestion is to find what is best for you. You do that by figuring out what is important to you and then go from there. In my own case, self defense, exercise, making friends, etc are on the list. Since you say you box, then adding footwork is a good thing. Likewise groundwork would help make you well rounded.

Some here will say MMA, Maui Tai, or other stuff, but the reality is you have to find what's near you, find a teacher and class that you like and that meets your needs. So take your time and go from there. Check out classes not only at commercial gyms but rec centers, gyms and even private homes. Don't rush into a contract and you'll find you'll find a great art.

For jumping kicks? Taekwondo, but because you said you know muay thai, it might be hard for you to get used to kicking with your foot instead of your shin. You still might not like it.

Based on what you said, first check out the Taekwondo place, and second check out the Karate place.

Taekwondo is what you are describing.

Taekwondo and your boxing will work great toghether.

Taekwondo offers better profficiency on the low body.

Take up Highland Dancing doing sword dance in bare feet

Thats lethal rights.

I want people that really know to answer please.I want to learn something with my feet more i know how to box i been boxing sents i can remember and i know muay thai but i would like to learn something like with the jumping kicks and all that. but i dont know much about karate or taekwondo wich one is better for me knowing what i know?