Seems like you’re conflating “analog” with “saturation”. That’s a false equivalency.
Saturation adds harmonics. There were many analog circuit designers that strove to keep the signal as clean as possible. They might start to soft clip when pushed, but at lower gain they were clean. Even audiophile tube power amps were designed NOT to get tube saturation at typical listening levels.
With saturation, you basically get 2 flavors - odd or even harmonics. Analog circuits can have unlimited flavors depending on circuit design and components used. You may like banana cream pie better than key lime pie, but they’re both still pie.
My understanding is the 32C EQ is not a saturator. The tape plugin on the mixbuses is the saturator. That said, the EQ does respond to varying gain levels. And in my experience, it takes some time to get familiar with. It’s not like any other EQ I’ve used. It appears the 4 octave bandwidth applies to the shelving filters as well as the peaking filters. Try running some pink noise through it into a spectrum analyzer, and watch how it responds as you move the filters.
So first, you may be looking for a specific type of saturation rather than an analog circuit emulator. Second, you may be looking for soft clipping. Third, you may prefer one analog circuit over another. Everybody has their favorite sounds that may come from specific analog hardware, or a combination of hardware units.
Use your ears, and good luck.