So long as you keep the training separate there shouldnt be a problem cross training.... what you may want to do is augment those striking arts with a grappling art as well i.e. jujitsu, judo, hapkido, etc. What you may discover when cross training at an early stage with similar striking arts, or just any striking arts, is that the methods and approaches to technique may bleed into each otehr, and you find your self making mistakes, if you know you can avoid this and keep the training separate then go for it.....