The MP-1 is a fantastic box. But I think it is best owned by someone who knows a little electronics and can do repair (desoldering, soldering). Or someone with a very good friend who is like that (i.e. will investigate and fix stuff for you for free, help you with mods, and give you advice, etc).
I have one of the oldies from 1987, with the top switch. I got it completely stock.
To get the best sound out of it, I ripped out about 7 op amp chips and replaced them with new NE5532's. (I have one more replacement to do: the LF347 quad op-amp in the EQ section, for an LM837). Good, new op-amp make a night and day difference. All of the usual complaints people might have about the MP-1 will disappear: it becomes quiet, with lots of clarity and high end. Basically, it sounds like a really good amp. That's exactly what people hope to get out of this unit: the pre-amp section of a good tube amp, but MIDI controlled. With a little TLC, the MP-1 can deliver that, and will sound much better than the day it rolled out of the factory a quarter century ago. Especially if in addition to the chips, you also take care of some passive components, like aged filter caps.
Also, I added a very simple gain mod which doesn't change the character of the unit, but makes it way more flexible. I ripped out the internal 25K OD1 trimmer pot on the main PCB, and replaced it with an external 500K potentiometer. (This value is overkill; probably a 100K would do just fine. Only the section of the pot you are dialing in is actually part of the circuit, not the total resistance. A 200K pot turned half way is exactly the same as a 100K pot turned all the way. That is why you can get away with sticking in a 500K pot in place of a 25K pot.)
With this control, you can adjust the MP-1 to different guitar pickups. If you don't have this, you have to reprogram the presets for a different guitar. For example, if you got to a weaker guitar (or simply lower your pickup height), you lose distortion, and your cleans become quiet and out of balance with your distortions. And for some guitar pickups, there just isn't enough gain. What this means is that even if you crank OD1 to 10.0, it is very hard or impossible to get the OD1 LED to light up when you strum the guitar very loudly. But with this external pot, you can calibrate for any guitar so that it's easy to get OD1 to light up when strumming loud notes. (That seems to be the ideal setting, though with this large valued pot you can of course go way beyond and abuse the overdrive circuit to get it to produce its own distortion. It's a very good overdrive circuit, much better than any OD pedal, by the way.)
When you're able to get more gain for use with lower-output "vintage style" pickups, that in itself opens up tonal possibilities. I think that the MP-1 sound has been stereotyped because due to the limited gain, it was only used by shredders with shred guitars that have high output passive pickups or actives.
The MP-1 was basically configured and marketed at the shredder market because that's what was hot at the time, and drove the sales of that type of equipment. Anytime someone says "my stock MP-1 has tons of gain", you can be sure are not using some Seymour Duncan jazz pickup, or a Telecaster with a single coil.
Once again something that could have been brought to my attention 7 years ago! Cheers, Lucius