No dude, don't start Karate. Its good you've got boxing, you just need to learn how to kick, grapple and use weapons. Muay Thai is great and your boxing would help you in it, Krav Maga is excellent as it will teach you everything you don't know and look at Escrima it is simply awsome and you learn weapons straight away!
Oh and some Karate classes have throws but these are usually stolen form Judo or Ju-jitsu. If you want a good throwing art do Judo or if you want weapons with that do traditional Ju-jitsu.