At least two different ways altitude can be handled:
1) Let thrust fall off in direct proportion to reduced air density - i.e. maintain the SL N1 or EPR values. Thus EGT(ITT) is little or no worse on a high altitude TO than at SL.
OR:
2) Boost N1 or EPR to maintain thrust up to some target altitude. EGT(ITT) will increase accordingly.
Most of the engines I have dealt with use the latter method. It is a negotiated power management between the manufacturer and the customer to keep from losing too much TOGW, balanced against increased engine wear & tear.
