So I looked a bit further, and found this expanding add-on grip(http://www.amazon.co.uk/gp/product/B003N3BRSA/ref=oh_details_o02_s00_i00), which looked like it could accept 3*AAA batteries in one of those circular 'battery cages/holders' Iin each grip, and since 3 rechargeables make up 3.6V, I thought I could modify it to increase battery power - which is why I started looking on Instructables, where I found the PSP section and saw polo99a9's 'ible (https://www.instructables.com/id/PSP-EXTRA-GRIP-AND-SOUND-joystick-bar-and-2W-spe/), which inspired this - my first ever Instructable.
Before I go any further, I must point out that this makes my PSP heavy - particularly top-heavy with the speakers above. The hand-grip helps spread the weight, but I could do with something more than it gives me. See step 4 for more details, and future plans.
This is essentially intended as Stage 1 of 3, and I hope not to actually alter the physical body/materials/internals, etc. of my PSP at all.
Step 1: What You'll Need
2) 2 long fixing-bolts from an old serial(?) cable, such as that used to plug your monitor into the back of your PC.
3) A drill, with a 4mm bit (a Dremel-type rotary tool would be better, because of the tiny space you're working on).
4) A screwdriver if your bolts, like mine, aren't made to be hand-tightened.
Step 2: Measure, Mark and Drill
Measure the width of your speakers' support plate (66mm, in this case). Subtract your 'bolt hole' measurement from this second (36mm from 66mm, here). Divide the answer by 2, and measure in and mark that distance from each side of your plate (15mm, in this case).
Take a square-edge, line it up with one of your marks, and measure and mark 3mm down for each one (this is where I went wrong, leaving my speakers slightly wonky).
Once you're happy with the position of your marks, carefully drill the holes on a SLOW setting to minimise 'slippage' of the bit (and if you can clamp your plate, and back the area with a piece of scrap wood, so much the better).
Step 3: Assemble
Once you're sure you've got them in the right place, tighten them up CAREFULLY (you don't want to strip the thread in the holes, in case you want to use a camera in future, for example). When the bolts are as tight as they'll go, try gently flexing the plate to make sure they won't slip out.
When you're satisfied the plate will hold, mount your speakers. Push them as far forward as you can, then look underneath to check the contact between the lugs and bolts. You may need to jiggle things about a bit, but you should aim for the lugs to squeeze under the bolt-heads for extra support.
You should also notice that the speakers themselves aren't directly in line with the control-box anymore, but are 'bent' back a little. This is not a problem and is, in fact, a second 'happy accident' that increases 'stereo separation' slightly, for improved directional definition.
Plug your cable into the PSP's headphone socket, spend a little time sorting out the relative volumes, and you're done.
The sound won't be fantastic, and probably won't seem much louder, but it's more rounded than the built-in stuff - especially on Wipeout.
Step 4: Issues and Plans...
If I can get hold of a couple more of the grips and some old, broken Playstation/Nintendo etc. controllers, I want to look at adding buttons to operate the PSP's shoulder-buttons via a see-saw (teeter-totter) arragement, as I find it too difficult (especially with the speakers slightly in the way) to make use of them in Wipeout.
I also want to return to my original 'mod' idea of adding batteries into the grip to extend battery life. My problem here is I don't kow what the middle battery contact does. I've read something about a 'Pandora' battery that was discontinued, but I don't know any more than that. I could connect extra batteries in parallel, except for that lack of knowledge. And I don't know how to produce (from batteries) the voltage AND current (5 volts, 2000ma) that my charger is rated at - or what current I can 'get away with'.
Obviously, the simplest way to increase battery life would be to buy a 3600mAh battery, but why can't I 'create' something bigger..?