What do you define as a "visit"?
I suppose you can at a given time each day (perhaps just before the files are rotated) copy all the log info from all the domains into one temporary file, and then run your own scripting, depending on what you define as a visit, to count the visits.
This is about as specific information as you're going to get from me; we've never done it so we've never looked into what specifically needs to be done.
So at some point it becomes a job someone else has done, and can tell you, or a lot of studying yourself as to what you need to do, or hire someone to actually do the analysis and/or the work for you.
Jeff
