It would be cheating, but I bet some incredible Big Threes could be made from 1940 Play Ball, augmenting the active 1940 players with the special HOF subset they added (Alexander, Johnson, Wagner, Jackson, Mathewson, Bender, etc.).
For instance, my original Big Three of 1935 DS Ott/Terry/Hubbell can get upgraded in 1940 PB to Ott/Hubbell/Mathewson. Williams/Foxx/Speaker isn't a bad Boston trio either.
In the case of the HOF add-ins, they didn't really assign a team, which I suppose opens the door to some additional flexibility. Or, if you are good enough to recognize the uniform in the photo, maybe that pins down the team.
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