The pyramid wavefront sensor has become an essential asset for extreme adaptive optics systems, as it offers a high sensitivity. Its main drawback remains its nonlinear behavior. Using a gain sensing camera and a convolutional model enables the tracking of the first order nonlinearities, called the optical gains. They can be used in the reconstructor as an optimal modal gain integrator as they express the loss of sensitivity of the system in presence of residuals. Knowing them also makes it possible to offset the pyramid and maintain this offset during a closed loop. This operation allows to compensate for non-common path aberration, to maintain an absolute tip-tilt for fiber injection and to introduce dark-hole maps for high contrast imaging. This study explores the behavior of the offsetted pyramid wavefront sensor assisted by a gain sensing camera, in simulation and experimentally with the AO-bench PAPYRUS. This bench, installed on the T152 telescope at OHP, has recently been upgraded to include an infrared imaging path. Preliminary tests to compensate for NCPAs by offsetting the pyramid during on-sky operation were carried out during the summer, using the optical gains estimation thanks to the gain sensing camera.