Ay, there’s the rub in triboelectricity :-)
As anybody who has tried to unpeel a stubborn roll of Saran Wrap knows, or tried to get a cut and wrinkled piece of that wrap unstuck from itself, yes the same insulating dielectric can assume different polarities of charge when touching itself.
I wonder if the polarities obtained thereby are random or if there is some way to force what they will be.
Trying to unstuck the Saran Wrap generates more static electricity (an imbalance of charge, actually). The static has little to do with the Saran Wrap sticking to itself, and more to do with pulling it that way.
When you wrap up something with Saran Wrap, what causes it to stick to itself?