Best amplification for Magico S3 newer version on your experience

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.

@OP. In my experience, the 509 does not sound as powerful as its rated specification suggests. You could try a Pass Int 250 for comparative purposes. If nothing else, it will demonstrate that not all competently designed amplifiers sound the same.

Depending on your budget I agee Coda makes very good underappreciated amps. They fly below the radar. Your room isn't that big  too but  high amperage they put out is rather robust. That helps with the lower listening levels. A #16 would be magnificent. (I too have the s5.5 and it is amazing) Good luck making those Magico's sing.