I'm glad you don't use Intralink which would make this a different
File>Backup is a good option. Different from File>Save a copy, Backup
asks for a directory, and puts the current object and its associates
into that directory. So, if you have drawing A which references assy B
which contains parts C and D, then A thru D will be found in the new
dir - very handy. However, if there's also a separate drawing of part
C, you'll have to open that separately to get it saved. Basically,
Backup makes copies of the current object plus all the objects that
are required to make it work - e.g. if you have a drawing of a part
open, it will copy part + drawing, but if you have the part open, it
just copies the part. What counts is what is the active window at the
time you do Backup, not necessarily what windows you have open in Pro
altogether, so activate the window that contains the "most top-level"
object you need to copy.
Just check using Win Explorer what files will be backed up to make
sure you got all you needed.
Another route is to use Win Explorer to do the task to begin with,
which might work better with more complex object structures - just use
Explorer to copy your whole working dir, then purge the copy (search
the archives for Spekan) to get rid of old files you don't need.