Is it possible to manually edit a monitor profile? If yes, what software should I use?
No. It reflects the current calibration so that’s not going to work and would be awfully time consuming until your next calibration invalidates the profile.
You can and should edit the calibration targets to produce the visual results you desire and the profile is then built upon those settings. See:http://www.luminous-landscape.com/tutorials/why_are_my_prints_too_dark.shtml