Here in Portugal, we used sports arenas and other such venues to mass vaccinate people: the highest number of people in a single day was just over 156K (if you scale that to USA's population, that's around 5M vaccine doses in a single day).
My 1st dose:
- arrived about 10 minutes before the appointed time: was notified via SMS about the time, date and place of the vaccination about 10 days prior
- waited about 10 minutes for my turn
- filled the form about previous medical issues, allergies and such
- entered the waiting area inside the arena but isolated from the area the vaccines were being administered: there were about 100 people there waiting to be called
- was called to get my shot about 50 minutes later
- was asked about any allergies and their severity, and they gave me Pfizer's dose
- was given a card with the vaccine's data (brand, lot number, etc) with the date and time for my 2nd dose (same venue)
- was told to wait 30 minutes @ a specific chair for any possible adverse reactions: they had someone specifically to clean the chairs (there were about 60 chairs there), as they got vacant
- done
My 2nd dose:
- arrived about 15 minutes before the appointed time
- waited around 5 minutes before being called
- showed the card with the information about my 1st dose
- entered the waiting area inside the arena: there were about 30 people there waiting to be called
- was called to get my shot about 15 minutes later: they were calling TWO people instead of just one, like with my 1st dose: they gave the shot to one person while the other sat in a chair just outside "the vaccine booth" (there were 14 "vaccine booths")
- was given a 2nd Pfizer's dose and given my card with both my vaccine dose's information
- was told to wait 30 minutes @ a specific chair for any possible adverse reactions: same as with 1st dose
- done
28 days between doses, in my case: both were free of charge.