What I would personally do in this situation -- given my limited experience -- is to maintain a single spreadsheet document with multiple sheets.
I include what it looks like in Google Sheets to add a (sub)sheet since I don't have Excel, but I'm told they function similarly.
Have one sheet dedicated to (and named for) each person then have them import to their own sheet. Then you can merge them together however you like once all is collected. This could be automated if it's frequently repeated but I don't do enough of that to know how. So long as each person just imports to their own sheet nobody will clobber the work of anyone else.
I'm sure there are more elegant ways to do this, consider mine a fallback if nothing better shows up.