i wouldnt say its impossible, just might be a little difficult is all.
just wire up the +'s and -'s of the slim battery cells to the + and - of the phats battery cell. (the grey lithium ion cell inside the plastic battery case)
did something similar on a cheap ipod lookalike and ive had no problems, it would just take longer to charge 3 batteries than one. but a total of 4200Mah would be pretty sick. that would be a couple days playing time for me, and i'd do it had i not used up my umd drive space for other mods.
but still i doubt its impossible.
EDIT:
i read the forum that sammy linked to and the brokenroses guy has no idea what hes talking about.
on my ipod lookalike i replaced the original 550Mah battery with a 1200Mah slim one, but just the cell, i soldered the cell onto the original battery's circuit board, and other than taking longer to fully charge, i have had no adverse effects, now i get about 2 days playing time for my music.
the same thing would be done here, except instead of replacing the battery with one of a higher Mah value, you are simply adding more batteries to achieve a higher Mah value.
laptop batteries are built that way, in mine each battery cell is 2200Mah@1.2v, and so they put 2 cells in parallel to get 4400Mah@1.2v.
capacitors are often used in the same way as well, if you look on a motherboad for a computer you will notice several capacitors connecting the same two planes, its just to increase the capitance so the voltages are filtered out.
i would probably want to do it with either 3 slim or 3 phat cells though since the 1200Mah cells will run ou of juice before the 1800Mah one and it might confuse the psp.
