Yes it is possible to have a higher cabin pressure than at sea level (i.e. a cabin altitude that is below sea level)
It certainly used to be carried out by maintenance on purpose for leak checking the pressure hull on the ground.
There was an accident that occurred to I think a USAF aircraft that was overpressurised on the ground - it resulted in severe rupturing of the pressure hull at the rear of the aircraft. I'll try and search for relevant pics and post them.
Kind regards
Exeng