i found away to store up to 32gb on a PSP slim, it requires no system updates or any modifications.
you simply buy the PhotoFast cr-3100 adapter which allows the PSP slim to recognize dual Memory sticks SDHC card.
this cost $49.99.
then you have to buy Two 16gb memory sticks SDHC cards which cost around about $41.99 apiece.
then i also found away to fit 64gb in a PSP slim (but is REALLY expensive), and it requires the PhotoFast
cr-3100 ($49.99), then it also requires another two adapter that fits in the PhotoFast cr-3100, and this adapter
allows you to fit two 16gb micro SD memory cards in each one, these are called Photofast cr-5400 ($24.99)
you'll be needing two of the cr-5400, one cr-3100, and four 16gb micro SD memory card ($107.99 apiece)
total cost fro the 32gb is about $133.97.
total cost for the 64gb is about $531.93.