How many copies of the DeLorean time machine co-existed in the Back to the Future series?
At some point in 1955, there were 4 of them. I put them in the timeline of the DeLorean.
- The one Marty used in the first Back to the Future.
- The one the old Biff used to give the young Biff the almanac.
- The one Marty used in the Second Back to the Future to fix the alternate timeline.
- The one hidden by Doc in 1885 and fixed by them later.
So, the travel is
- from 1985 Marty goes to 1955 and goes back to 1985
- from 1985 Marty goes to 2015
- from 2015 Biff goes to 1955 then back to 2015
- from 2015 Marty goes to Alternate-1985 then to 1955
- from 1955 Doc goes to 1885 and leaves it there until it was retrieved by Marty in 1955
- from 1955 Marty goes to 1885 and finally to 1985
As indicated by NominSim's comment this timeline illustrates where people and the DeLorean are throughout the trilogy: