Jcm800, v4 or v5 op-amp muff or one of the clones, including the excellent EHX reissue which you can pick up for like $60, layer and repeat.
Strat with hotter pickups can help, they used Lace Sensors but those aren’t magical
It’s a simple tone really. Listen to Billy’s EHX video, guitar, pedal, JCM..... there it is, or at least as close as it gets in a single track.
Billy says that he stacks pedals in his Guitar World interview that's titled "Guitar Geek USA":
"Sometimes, though, a nice lo-fi pedal is just what you need. When we did "Siamese Dream," I developed a technique of plugging my Big Muff pedal into the low sensitivity input of a 100-watt Marshall JCM 800, with the master volume on full and the preamp volume barely on at all. To me, the Electro-Harmonix Big Muff produces the ultimate super-gain VROOOM sound. Live, however, a Big Muff doesn't give you enough definition. I just keep experimenting with different combinations of pedals--and guitars--to get the ideal sound."
The EHX opamp reissue is a good pedal, but it doesn't sound exactly like the original V4 opamp Muff and has its own character. The BYOC opamp l'il beaver is said to be an exact clone of the V4 opamp Muff. I have both, and they stack well together. I also have a couple of other Muffs, and various other fuzz' that stack well with the opamp Muff.
Stacking one Muff into another brings the sound far closer to the SD sound than what's heard in the EHX opamp Muff reissue video. I can get all kinds of SD sounds that are basically like it sounds on the album by stacking 2 - 3 pedals.
There are a lot more pedals than just the Muff being used on the album including the Micro Synth, an MSA circuit (that was removed from a pedal steel guitar and put into a custom pedal enclosure), a SuperFuzz, and the MXR Distortion II. One article cites Butch as saying that Billy also had a litany of DOD pedals. Billy is also known to have used a TS9 in the Gish days and might have used one on SD.
The MSA pedal steel fuzz circuit that billy used on SD and also used heavily on MCIS is possibly the Jordan Bosstone circuit that is available for purchase as a standalone pedal.
The Micro Synth, in addition to being used on leads, was likely also used on rhythm tracks. There an interview where Butch says that Billy was using it to carve out sonic space in the mix for all the many guitar tracks.
One of Siamese Dream's sound engineers, Jeff T, said during the GearSlutz Q & A with Butch Vig that he recalls there being lots of SuperFuzz on Siamese Dream.
Jeff T also mentioned that Billy used a ring modulator on Rocket:
"On Rocket, Billy used a Ring Modulator...he actually used that quite a bit I recall. Cherub Rock, I'm not so sure. I do know that the FX on the solo was actual tape flanging between the 2 tape machines."
I think that the 1992 unreleased live track "Cinder" is an example of Billy's KT88 JCM 800 simply being overdriven by a TS9.
The Cherub Rock rhythm sound is the MSA pedal steel circuit overdriven, running into a Big Muff, or vice-versa.
The grindy Today rhythm sound is a SuperFuzz running into a Big Muff, with the volume level on the SuperFuzz very low to avoid it splattering like it does.
Think of it this way, if there was a certain amount of gear, or pedals etc that would nail the studio tone live, Billy would use it. He’s got all the resources in the world and he doesn’t get that tone live. No one does, because it’s a studio tone.
Big Muffs are notorious for not working in a live situation because they don't cut through a mix, and Billy has said they tried to use them live and they just got lost in the mix. So, they didn't use them live anymore.
He also touched upon that in that same Guitar World interview:
"Live, however, a Big Muff doesn't give you enough definition."
I’ve actually seen a few clips where guys did like 10 overdubs using the EHX op-amp reissue and it’s spot on. Cheap muff, lots of layers, priceless tone.
The rhythm guitars parts on SD are quad-tracked. Example: 2 Strat takes hard-panned to one side, and 2 Les Paul takes hard-panned to the other side. The guitar takes were recorded with an SM57 and MD421. Some takes were recorded using an API lunchbox, and some using the Neve preamps in the console.
Butch likely also mixed the guitar parts like he demonstrates in this video for a track on Nevermind, with 2 guitars hard-panned left, 2 hard-panned right, and one guitar in the middle:
Butch comments on that style of mixing in his GearSlutz Q & A:
"When I put a guitar up the middle, it usually has more mid-range crunch, or try to find a eq pocket that gives definition to the chords or riff...and it's usually in the mid-range, 500 hz to 2k..."
Billy has said that the basic lead sound for SD is an MXR Distortion II into a Big Muff, and that an MXR Phase 100 was use to give the lead sound a bit of movement. He says that in this video:
Billy also said in his Guitar World interview titled "Guitar Geek USA":
"Finally, the nasal, squeezed-up lead tone that I use so often--as on "Pissant," for example--I ripped off from Michael Schenker! I used an Electro-Harmonix Micro-Synthesizer and some unknown fuzz pedal, plus an MXR Phase 100."
The "unknown" fuzz pedal he mentions could be the MXR Distortion II... I'm not sure if it was a popular pedal or not... but is likely the MSA pedal steel circuit that Billy had transplanted from a pedal steel guitar into a custom guitar pedal enclosure. That same MSA fuzz circuit was used all over MCIS, and can be seen in its custom pedal enclosure in many videos of MCIS live tour shows, typically sitting on or next to Billy's Orange amp, next to a Roland Double Beat (which is another pedal that stacks well with a Muff).