Thanks everybody for your opinion, an AVR could be a way to go, with my budget the best I can get is a Denon AVR-X2300W, a Yamaha RX-V681 or a Onkyo TX-RZ710, I'll start to look for these too.
Going back to the main topic I see the A-S701 is a well respected piece of equipment, which kind of confirm all the good I found on this amplifier. I think paired with the Schiit Modi Multibit should reach very good results in music playing.
@Bucknekked I didn't specify what I'm using right now because I'm quite sure no one ever heard of it, the Alientek D8. It's a small FDA (Full Digital Amplifier) that sounds impudently well for its size. Out of the box it's a bit bright and edgy, but upgrading the power adapter makes wonders. Maybe you saw the FX Audio D802 on Z-Reviews, it's available on Amazon.com too, that is a very similar amplifier that uses the same STMicroelectronics chip family. The D802 has the STA326 while the D8 has the STA328, there are minor differences between the two.
If you are wondering why I'm looking for a new amplifier despite the fact I like my D8 that much it's because even if I think D-Class is getting better day after day (look at Denon PMA-50, NAD D 3020, Peachtree Nova 300, NuPrime IDA 16 and so on, just to name some) and these cheap Chinese FDA are the way to go for whoever is looking for a cheap amplification with good performance and digital inputs, I feel like AB-Class has still the edge for smoothness and musicality (all of this rigorously IMHO).