Moving to separates

… but an amp is about the only thing that seems reasonable

High-end audio is a small niche market above box store offerings, and can get very expensively “unreasonably” quickly. For Sonics, the entire audio chain matters: including source(streamer+DAC), preamplifier, amplifier, speakers, and cabling.

While the OP seems to have a great surround system, simply switching from the internal Integra amp to an external amp will have limited effect as the rest of the audio chain will likely limit Sonics. Usually it’s much better to split surround and 2channel audiophile systems as it’s extremely difficult to lift 2 channel Sonics to satisfying levels.

So to answer the OP’s question a better amp would likely be sonically better, but trying to squeeze great 2 channel sonics from a surround system is extremely difficult as better 2 channel components simply perform better.

I should clarify that on my computer I have a mix of stereo and 5.1 music, and they play randomly and intermixed.  Windows is set to 7.1.  Kodi upmixes songs to 7.1 automatically given whatever the current song contains.  I know most of y'all seem to like stereo music but I would never give up the surround sound.  Even when upmixing is required, it sounds much better to me.  And songs that are mastered to 5.1 are absolutely fantastic.  Envelops me from all directions.  This is why I am resistant to streamers, integrated amplifiers, and moving away from the Integra + Dirac.  Sounds so good, I'm not even sure I need an external amp.  Would be a real bummer if I spent the money and couldn't tell the difference.  Money might be better spent on speakers. Or a new house, lol.

Buy a good intergrated amp, more bang for the bucks.

An interesting topic.  I do have seperates, mono block s/s amplifers and tube pre amplifer.  I am now testing an integrated platform and have been impressed!  Not all assumptions are true in audio.  This is enough of a postive change to move me to the integrated.

Thanks for clarifying — that helps a lot. Since you listen to multichannel music I’m gonna reiterate my recommendation for the McCormack amp I linked above, and for only $800 I’m confident you’ll hear a substantial improvement over the amps in your AVR.