Yes, in fact switching grips is encouraged also do wide, narrow, put a towel over the bar, and use that even try using a thinker bar will make things harder on the grip. Same thing with push ups vary the width of your hands and the elevation of your feet. Another awesome thing you can do is use rings. I personally use rings for push ups pull ups dips and many other they are intense.
Just be sure you give yourself adequate recovery time. Liston to your joints, nothing worse than making taking two steps forward only to need to go back 3 to wait for tendinitis to heal.