That cannot be done. Newton's third law applies. The force of the rider's foot on the pedals is always exactly equal to the force of the pedals on the rider's foot.My question is about what happens to power output when you stand and apply that greater downward force WITHOUT changing gearing/resistance - i.e., - when you increase downward force without a increasing the opposing force?
However... For a fixed gearing, as the force exerted on the pedal increases, the speed of the pedal will increase. As the speed of the pedal increases, the cadence increases. The amount of force that a rider can apply may drop as a result.
Like throwing a feather, will be dissipating effort moving your hand instead of moving the feather.