I managed to dig up the technical service manual for the 876.
The diagram is a fairly standard (and reputable) NE5134 with class A buffer stage design.
So in terms of design it is a good one certainly up with $200-$300 headphone amps and perhaps better due to the ample power supply.
Constraints are most likely:
1) Noise generated by the digital circuitry filtering into the headamp (through the psu, ground or by EMI/RFI ?)
2) DAC quality.
I think the biggest question mark is DAC quality, and the two main factors in that are PSU quality (Noise, ripple etc...) and Clock accuracy. (And Clock accuracy is often associated with PSU as well...)
I have not had the ability or opportunity to Audition a true benchmark DAC to compare to the Onkyo, so I can make no comments outside of that....
But it is a good sounding box, and although I purchased a Matrix Headphone amp - I feel that it is not a huge "wow" step up, but it is in fact a step up. (possibly simply due to the seperate PSU, and seperate circuits - greater distance perhaps from the digital noise?)
Also the Matrix allowed me to "play" with different opamps and opamp biasing into class A - which also improves Sound Quality... so another incremental step up....
BUT - the Matrix is a $300 headphone amp + opamps and adapters $60 - so it is a $360 heaphone specialised amp, versus an AVR that can be purchased still under warranty for around $600.... and has a headphone amp, power amp, ADC, DAC, surround processor etc etc... it is to be expected that the Matrix outperforms the Onkyo AVR - what is truly remarkable is by how little it is outperformed.
bye for now
David