Not very much. The SNES was the king of stuffing coprocessor chips onto cartridges; the hardware was a minor 6502 upgrade paired with amazing sound from Sony, and some pretty good video hardware. Sega did almost the opposite: they took the 68000, a pretty good CPU for the time, and paired it with OK sound and a tweak to the TI VDP they were using in the Master System. The average SNES game just needed the extra oomph that a coprocessor could give, while the average Genesis game probably was fine with the 68K.

That's not to say coprocessors didn't exist. Sega loved expanding the Genesis - but with hardware-addons that didn't sell very well. The Sega CD is effectively a second console's worth of coprocessors. It included much-improved audio hardware (which barely got used because you had CDDA), another 68000 CPU, and some fancy rotozoom ASIC stuff. There is a SNES style "just sneak a chip onto the cartridge" thing, though, but there's only one game that does that: Virtua Racing. It has a very primitive hardware rasterizer on board, which actually causes problems with some later-model Genesis consoles. It also won't work at all if you have a 32X plugged in.