Can I combine running,muay thai,bjj and wrestling with weightlifting?

I want to join this gym which coaches MMA and to increase fitness I plan on increasing my weekly runs. Before I had Muay Thai once a week,a 2 mile run and a day at the gym which involved heavy weights (3 sets of 5 reps). Would my gym progress suffer by increasing my weekly 2 mile runs as well as adding all of this? Or would by strength decrease as a result? I hear that running too much decreases muscle and causes you to become more lean!