I have trained in multiple arts for decades. I began Judo and JJ as a child in '71 until my instructor quit teaching. Then, I trained in American Kenpo at one of the Tracy's schools until it closed it's doors. Then a TKD/Hapkido school opened a few miles from my house by a then unknown 2nd dan named Ernie Reyes, Sr. and his partner Tony Thompson. That school stayed open and 33 years later, I'm still their student.
When I first started training under them and their master instructor, GM Dan Kyu Choi, it was strictly a traditional Korean school (old school). Within a couple of years, they broke away from GM Choi and started incorperating the FMA's into the advanced curriculum. KJN Ernie was one of Remy Presas' first BB's in America, then we actually had the West Coast Escrima Society having their classes on our second training floor with people like Mike Inay, Jeff Elliott, Jimmy Tacosa, Dan Inosanto, Richard Bustillo and GM Max Sarmiento as members. Being an assistant instructor and having the key to the school, I was often training after class and was the one to lock up.
In 1980, KJN Ernie did an exhibition match with Benny Urquidez who introduced him to Muay Thai...the hard way. After that, we all began training in Muay Thai, first with Benny and much later with the guys from Fairtex. We did some work in various forms of Japanese JJ with Sid Campbell and Wally (and later Leon) Jay. Then, Ralf and Cesar Gracie moved to the USA and had teaching programs in our schools and BJJ became a part of the curriculum.
When Frank Shamrock moved up from LA to San Jose, he started teaching the MMA and Grappling classes on Mon. and Wed. mornings. For a while, his protege Bob Cook (head MMA trainer at AKA and UFC veteran) took over, but Frank is back on Mondays at least. From this base, I took the silver medal at the NAGA World Grappling Championships in the Expert Super Heavyweight Division.
To make a ridiculously long story short, cross training is and has been a requirement in our schools for over 30 years. It has made me a FAR greater martial artist than I EVER would have been without it. I do recommend that you develop a good, strong base in your parent style and then enjoy the growth.