Forgive me if this deviation from OTL has been previously covered but I have searched and can not find a reference. I've recently being doing some work on police strikes (Boston, London, Liverpool and Montreal) and found several reference to hands-on intervention in the strike in September 1919 by Coolidge, then the Mass. Governor. Given the fairly fluid state of things on the night of 10/11 September, the disparate nature of the players (1300 striking police officers, auxiliary police, Harvard student volunteers, state militia, anarchist activists, the usual Irish and Italian mobs etc (apologies)) it would not be unreasonable for Coolidge when visiting the scene of say, the Scollay Square riots to become a victim of a bomb or shooting either by accident or design.
If Coolidge had not been available for nomination at the 1920 Republican national convention who would have taken the VP slot? Is there a possibility here for a younger FDR to join the ticket. If this was the case, then we would have had FDR as president in August 1923 rather than January 1933. Implications? As my old politics tutor used to say: "Discuss"!