Good call on the Jam, the Police and Stray Cats. 
I am going to add the Minutemen.
I’ll vote for Van der Graaf Generator, who have been a 3-piece since Dave Jackson (flute/saxes) left in 2006.
They’re now piano/guitar, organ & drums!
Their sound isn’t quite as full but still pretty good - they’ve released 5 studio albums and toured several times as a trio, although I’m not at all sure they’ll tour again as a group - they’re cracking on a bit and all three are in their mid-70s now)
Rory Gallagher‘s great power trio, Taste.
Gotta be Rush for me. . . but, don’t forget Grand Funk Railroad. They were huge for decades. Never owned an album though.
I saw them with a sign saying “The original 5-man trio.” There were 4 band members.
After just now rewatching Monterey Pop, I’m gonna say Ravi Shankar and his two accompanists.
Respect.
Well, Rush is my all-time favorite band, so … yeah.
In the last few years I’ve become a big fan of this Japanese, 3-man metal band called “Ningen Isu”. Very Sabbath-influenced, but they really do their own thing. Guitarist Shinji Wajima, bassist Ken-ichi Suzuki, and drummer Nobu Nakajima. All three sing, though Wajima handles most of the lead vocals. Wajima and Suzuki have been there from the beginning; they’ve had a handful of drummers, but Nakajima has been with them since 2004. Twenty-three albums since 1990, finally started getting attention outside of Japan in 2020. Wajima is the ultimate riff-master.
This, and also Rush, King’s X, and R.E.M. from 1997 to 2011.
Ningen Isu. Sounds interesting. Looking into it.
Thanks.