Yup, we do that on our (soon to be phased out) boeings. Double derate (derate plus ATM) and manually selected climb thrust, either one step up or full climb thrust. It saves money during take off dur to lower engine lease costs, and money during climb out as it gives the shortest possible tome from thrust increase altitude until top of climb.
The small busses dont have derates and so far i havent encountered a thrust increase at reduction.