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I saw the Four Tops this summer, not because I am a big fan, but because their opening act was a friend. There were three distinct "units" on stage. The headliners were the four vocalists, one of which was an original member and one of which was related to an original member. Then there was the core rhythm section - guitar, bass and drums. Then there was the "music director" who played keys and also directed the remaining unit - about 9 horn players. Everybody was introduced by name at some point and there was nothing I heard that suggested recordings or offstage players were involved. I think the vocalists, rhythm section and music director toured together. The horn section was doing several East Coast gigs with them but not the whole tour. While researching the "nostalgia concert' business I discovered that there are may acts touring on the strength of a big name but everyone else on stage could be locals hired for the occasion. When I was still in school there were a lot of family friends in the musician's union and it was somewhat common for a big act to come into town and supplement the act with locals hired for the gig.
https://www.classicalbumslive.com/ is one touring band that sets out to reproduce the sound of an album live, on stage. They generally do not feel constrained to use the same number of musicians as the "band" they are covering.
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Since the driving question could be paraphrased as "best 3 person ensemble" I might consider qualifying that as "an ensemble that performed live with exactly three players" - no one hiding off stage and no prerecorded parts added to the live performance.
If I have sucked all the fun out we can decide at what point a reliance on pedals and effects constitutes an additional performer (loopers, delays, chorus, harmony?) and whether there are any acts under consideration that performed live after 1980. Alternatively we could discuss the Rise and Fall of the "Power Trio".