I would like to know if it is possible to capture multiple versions of the same
website with one WinHTTrack Project; a clear solution to me is to simply
create a new project every time I want to update a site, but, at the chance of
convenience, I wonder if it can be done with one project.  

This would involve creating a cache of the website every time you update it,
so that it does not overwrite old/missing files.