Originally Posted by
ersatz
Eat all you want, it won't help. The fact of the matter is that the combination of both will very likely have you on the edge of overtraining. I wouldn't lift more than 3 times per week especially with MMA training 4-5 times per week. Recovery will be difficult so you'll have to experiment to find your balance. I would start off with two total bodyworks a week and see if that suffices. If not a 3 day split might be ab better option.
Diet is especially important and amino acids will be of great value. I'm not entirely sold on the importance of carbs pre or peri workout and generally tend to avoid them.