Can a ecu tune change the peak output of an engine

To get more power then what it already had so you can say my car makes this hp and torque now and not that anymore, gains in the power band are good but better not fall below stock levels.

Another question this might be a noob one but go with me I know a transmission gearing and the diff ratio equals to the amount of engine revolutions at a given speed. But when a engine peaks its hp at 5600rpm and tq at 4400rpm, but redlines at 6500rpm does it mean that a tune will only raise power at these rpms due to the camshafts. I was thinking if a tune could raise the hp to a new peak of 6400rpms for more power up top and more torque than before.

reprograming a computer is done to alter the fuel and spark curves. From the factory, things are tuned a little rich and the timing slightly retarded. This is for three main reasons; 1) emissions, 2) detonation resistance, and 3) as a cushion for bad fuel, dumb drivers, or other parameters.

Retuning these fuel and spark maps can often make a little more HP and TQ but often require premium fuel. The RPM at which the torque and hp peak is relatively fixed. That is a function of cam, head flow, and exhaust flow.