I have different speakers to your (Gallo Reference 3.2) - so consider yourself "pinch of salt" warned
When I first purchased them, I had read reviews, that pointed to the 8ohm nominal spec, and used low power valve amps, waxing lyrical about the characteristics of these speakers.
Other reviews mated the low power valve amps, with a seperate high power amp for the woofer (they are wired for true bi-amping, and gallo used to sell a specific amp for the purpose)...
Anthony Gallo himself used to demo these speakers at audio shows with a Spectron Musician amp ... 500W @ 8ohm, doubling into 4 and then again into 2 ohm.... so both very powerfull, and VERY high current....
I had run the speakers with success using Onkyo/Integra flagship AVR's (140W@8ohm spec, measured in various tests to do over 165W@8ohm clean... current limited below 4ohm) - and some Quad 606 amps (another high quality 140W@8ohm amp).
Further investigation on my speakers showed that they drop down to just under 3 ohm at the woofer, and around 1.6 ohm on the tweeter - so there is good reason to assume they might do best with an amp capable of substantial current.... so something that is well rated and has plenty of headroom when supplying the desired speaker voltage (SPL) at those low impedances.
Searching through amp specs for something that approximates the Spectron Musician's specifications, without requiring a home mortgage to purchase... I came across the Crown pro/pa amps XLS2500 (440W@8ohm, 775W@4ohm and 1200W@2ohm) - grabbed a pair of these used... to try out.
The end result was interesting - compared to Flagship AVR, and high quality traditional amps (Quad 606) the Crowns were slightly better... not chalk and cheese by any means - but the tendency was in their favour (before anyone asks, no there was no blind testing, and yes it might be confirmation bias... on the other hand, I was biased towards the Quad amps... and this comparison did not go in their favour!)
More recently I chose a step down in AVR terms, as I did not require high power from the AVR, but I needed high quality DRC and wanted to try Dirac... the Integra DRX 3.4 has only 100W@8ohm - and Amir has shown it shutting down with 4 ohm loads under stress.... clearly NOT a high current design.
Connecting it to my speakers, and running at a mere 75db SPL at MLP (which calculates out to around 1W average with peaks of perhaps 16W for 20db headroom) - the soundstage was confused, imaging was shot, sound was "veiled" - connected my Quad 606's or the Crown XLS's and the sound immediately cleared up.
So what general conclusions can be made?
1) AVR's in general are current constrained (but so are many power amps!)- if your speakers are current hungry, it may affect the sound quality negatively even at power/spl levels that one would normally assume would not have an issue. (why this is the case, I am not sure... but the subjective listening results I get are consistent)
2) External power amps driving the main speakers can result in noticeable improvements in sound - sometimes ever with amps that aren't obviously superior to the specs of the internal AVR amps.... again this may relate to taking load off the internal power supply - but it is not always the case - TOTL Flagship AVR's are a bit of an edge case - and often have much more substantial power supplies and amps, than their mass market brethren
3) Some speakers, seem to like an amp with massive reserves... even when these are NOT used - the overall sound is better (the Gallo's do!) - other speakers, this sort of excess has no impact whatsoever (I used to run Quad ESL's - and although sensitive to chain quality, they were never sensitive to "power" - not a much current required on that design)
4) Know your speakers, and if possible, experiment with alternate power amps... I took on the Crowns as an experiment, with the option of reselling them (possibly at a profit, given the great price I got them for) - but they surprised me, and have remained in my setup - for 10 years now.