Best amplification for Magico S3 newer version on your experience

I have the A3's. The best sounding amps I've tried are high amplification SET mono blocks. I'm finally at audio nirvana with NAT Audio Magma M mono blocks. 

A buddy has the S7's. He has VAC 450iq Statement mono blocks. He once told me that in order to get Magico right you basically need to spend about double on amplification in relation to the cost of the speakers. 

The best Magico sonics I've heard have always been paired with high output tube amplification. I also agree with other audiophiles I've spoken with that 4 ohm speakers need tremendous power coupled with at least moderate volume to sound their best. 

FWIW I’ll give you my experience for driving a pair of Magico S5’s. I started out using a Luxman m900u. I thought it sounded great. Then I switched to a Coda S5.5 amp as I’d had the Luxman for a long time and had the itch to change to something new. The little Coda outperformed the Luxman in every way. The Coda is only 50 watts class A into 8 ohms and doubles to 100 watts at 4 ohms and can drive a 2 ohm load at 200 watts. I think the key to its ability to out perform the Luxman is that it draws 100 amperes which a lot more than the Luxman even though the Luxman is 150 watts into 8 ohms and 300 watts into 4 ohms. The little Codo retails for $6,400. I recently saw a used one for sale on either this site or usaudiomart.  That’s just my experience. Good luck!

I've never heard the S3s, but the CAT amps sounded amazing on the S5 MkII

The S3s are a difficult load. For a relatively cheap amp I'd try the Schiit Tyr mono blocks. They have a huge power supply for the money using chokes(which produce super smooth current) needed for the large current draw for the S3 load. Power supply cost money and doesn't show up in specs. One of the things you get in costly amps is huge power supply because they can afford it. But even six figure amps don't use chokes and perhaps they should.