You can overclock by increasing the multiplier in the bios, like you would on any other PC. But I would not recommend this and its fully at own risk if you do. Alternatively you can replace the CPU by a faster one. These old CPU's are very cheap. I once replaced the celeron 566MHz with PIII 733MHz and added extra memory. Socket 370 Celeron / PentiumIII (FCPGA type) 300MHz~1GHz Memory168 pin DIMM PC100/PC133 Up to maximum 512MB FSB133MHz/100MHz/66MHz But if you own the Pentium 233MHz MMX model, you are limited in upgrade options.
...Unless you buy the better PCI card separate from a dev kit. Chances of that popping up are slim to nil, but it's worth looking out for if you have a 233 card.
I really don't think Sony designed any such mechanism to overclock the EE even in the PS2 Tool. The PC debug card can be overclocked but it doesn't cause any games to run any faster at all. At best the benefit is increased throughput for the debug side of things.
You probably won't dare to do it if you have lost a SCPH-10000 before due to cracked solder joints. And it has the exact same EE chip as a TOOL. D:
But if he overclocks the EE, won't the solder on the mainboard be subjected to increased strain? I thought of it from the direction of an increased likelyhood of thermal shock. :/
I think the fault you experienced on your 10k (and I on my 15k) actually has more to do with design problems in the clock synthesizer chip itself than anything else. Another thing, each generation of the PS2 chipset SONY experimented with the clock generators so each generation used something different. SCPH-10000 has two completely separated clock generators, each one with a separated 18mhz clock source (feels like it was a rushed design really... as newer units use a sort of cascade to avoid using two identical oscillators). As per overclocking, overclocking a PS2 is nearly useless and have a collateral effect of raising clock on the IOP and sound hardware.