I am using a .4 mV MC cartridge with an MM input in Santa Cruz. It is an old Sony TA 4650 with a VFET MM input stage. I then route the signal into a Yamaha surround receiver for ambience processing, and it works and sounds absolutely wonderful. I have tried also using an adaptor with the headphone output of the TA 4650, which is taken off the VFET push pull amplifier stage, and it adds about 20 db of gain, but it sounds great either through the preamp output or the headphone output, either way, no audible noise or liability that I can discern.
There is nothing that says theoretically it would not work out OK to use an MC cartridge since you still get the RIAA equalization, you may need extra boost down the chain, and I would imagine it would be cartridge dependent. Lower gain MC cartridges would be subject to experimentation. Every doubling of voltage is about 6db of gain.