No rocket science here.
Find the 'fully charged' voltage of the PSP go battery.
If it is 4.1v or 4.2v, lipo will work.
Then find the fully discharged voltage of the battery.
Is it above 3.0v?
Remember that lipo can charge from 3.0v to 4.2v. The meat of the charge is at 3.8v, so losing 0.1v is no big deal.
I would say only parallel the cell if the cell mAh is similar.
Another idea is to take some lipo cells and tape them on the back. Hook them up to where the stock battery was connected.. and create a protector out of plastic or ABS for the batteries so that you don't drop it right on the cell accidentally.. lol.
Yeah it would be ghetto but you could have 4x or more the battery capacity..
On the downside the stock charger would take forever to charge.. lol. it probably charges at a rate of 0.5amps or something.