No, FCP doesn't have a user initialed increment and save.
you can of course do a "Save As", and manually enter the date & time.
then you wind up working in that new project.
is that what you want?
if not, then what i sometimes do is ANOTHER save as,
click on the original project file, and that updates your save-as project name.
(or you could strip the date & time manually)
then i overwrite the original project.
only takes a few seconds.
if your projects aren't huge, then it should be simpler to simply duplicate the SEQUENCE in the project.
one thing i like to do is to dupe the sequence in the browser, (right click on it, and chose "duplicate", or Option D)
so "EDIT 3" becomes "EDIT 3 copy"
then i re-name EDIT 3 to EDIT 4 and keep on working in the same timeline.
(there are plenty of variations on this idea, of course)
you could pull up the "last modified" column in the browser if you want a time reference for the older sequences.
cheers,
nick