You would need to set up either a single channnel EQ for each channel, or three dual channel and a single channel, and then a parametric for the Sub. Only reason that I can see using a EQ over the software of the avrs, is if you are like me, and want more control of how the sound is tweaked vs. just going with the standards that the manufacturer has set up.
Also, you would need a separate amp for each channel, a pre-amp vs avrs with amp, a compressor/limiter with delay, so you are talking a few thousand dollars for a decent setup. If the software that your AVRS has for tweaking the sound is doing its job, stick with it for 7.1. If wanting better sound for 2 channel, for music, and that is all you are listening to, go with a decent eq or parametric.
Keep in mind, that a lot confuse the use of a equalizer, whether non-parametric or parametric, with only being used with a sub-woofer, or in live settings. I use a parametric, so that I have better control over how my music sounds, along with tv programming, since all I use is a 2 channel set up, and can get better control than with a non-parametric 31 band graphic.