I don't think there is a way to change the time control for "each move" but you can easily change the "total" time. When you send a challenge in "live chess" you can change the time control near the upper-right. In the preset times, 1 hour (per side) is the maximum I think, but clicking "custom" allows you type in ANY time (including longer if needed). Alternatively, send a "daily" chess game where each side has literally days to make a single move! (that is the closest I can think of for "per move").
I hope this helps, but if details are wanted: feel free to message me and I'd be glad to help. 
Brand-new here at chess.com. Wanting to play my nephew. Is there anyway to change the time settings so that the game doesn't end after 10 minutes of time? Can't we just put a timer on each move (not the total amount of time each side has to move)?