Is it possible to take 3 or 4 identical spreadsheets, each identical in
design, but with unique data and merge them into one?

This would be used to count votes in a local election. There would be
approximately 46 precincts in the spreadsheet, and four people would have
identical copies on networked computers. They would enter precincts one at
a time as they are called in, with results for each precinct ONLY being
entered by one of the four operators.

I'd then like to merge (or add them together) to get running totals.

I hope this makes sense, and thanks for any advice.