I'm a Thai/American, a long time Tae Kwon Do practicionar, and a student of brazilian jujitsu and judo.
In my opinion it's a great idea to cross train with western boxing or muay thai. In fact I've been training in both arts since I was a child. TKD offers an awsome kicking arssenal combined with speedy foot work and Muay Thai can complement with powerful knees and elbows for close quater fighting.
Good luck and always contiue to train hard!