The moving magnet input is rated at 3.3mV and the moving coil input is rated at .6mV.
A cartridge rated for 2.7mV would require the volume control to be raised slightly higher for a given volume, but there is nothing that is going to be harmed by doing this.
Power amplifiers are standardized for 28dB of voltage gain, but the exact relationship of the 3.3mV and .6mV rating to full power output from the receiver is not part of the specs, but a guess would be that is the voltage for full output with the volume control at maximum.
Cartridges fall into 3 categories - moving magnet which are typically rated for 5mV output, "high output" moving coil cartridges which are rated for about 2.5mV, and "low output" moving coil cartridges which are rated for about .6mV. The phono input sensitivities of the receiver should be able to accommodate all of these without any problems.
Back to the original question, short of buying an outboard phono preamp with more gain, there is not much you can do about the situation but accept the higher master volume setting.