sounds like you want to start doing UFC type fighting also know as mixed martial arts, you have to look for places that host that type of training, go to your local martial art location and ask about a recommendation for a location
"Traditional Muay Thai has a long history in Thailand as a martial art used by the military since ancient times. The military style of Muay Thai is called Lerdrit, while today's "Sport Muay Thai" slightly varies from the original art and uses kicks and punches in a ring and with gloves similar to those used in western boxing. Muay Thai is referred to as "The Science of Eight Limbs", as the hands, shins, elbows, and knees are all used extensively in this art. A master practitioner of Muay Thai thus has the ability to execute strikes using eight "points of contact," as opposed to "two points" (fists) in boxing and "four points" (fists, feet) used in the primarily sport-oriented forms of martial arts. Muay Thai is an especially versatile, brutal, straightforward martial art"
Yeah. Muay Thai is fucking hardcore too, but if you want more defensive type skills than go with Jiu Jitsu b/c Muay Thai is fucking crazy bareknuckled fighting to the knock out.