As per the title, I’m in search of an amp that can power 3 or more pairs of speakers simultaneously.
I haven’t been able to find any yet.
Your help is much appreciated. 
Unless you need specific control over those speakers, you can hook them up in series/parallel depending on what amp you have and the speakers.
Just be careful with the impedance.
Otherwise, you’re gonna need a PA amp. Most likely a rackmount style amp.
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I see, thank you for your reply, will explore that option!
I have a Sonace 260x3. Lots of these kind of amps out in the world. Ex-McMansion installs often.
You probably need to look for Rack Power Amplifiers.
Dont know are there 6-channel options but 8-ch options are plenty.
Or split the signal chain in 3 separate, similar amplifiers = 6 speakers play.
Much is budget dependent.
The biggest Amps I know channel wise are 4 channel (= 2 pairs of speakers).
Apart Champ Four or QSC PLD series for example.