You can switch on the "Share Workbook" feature from the "Review" menu. This allows multiple simultaneous users - however it still doesn't do exactly what you want. In this mode, you cannot change the layout of spreadsheet (add/remove rows, etc.). If two people edit the same cell, you get a conflict dialogue not a new row.
I do not believe that Excel is the correct tool for this case. If you really need multi-user live editing, I'd try a different tool, perhaps Google Docs may be closer to your needs, the multi-user editing in that is pretty good though it still wont create a new row on a conflict, I don't know anything that will do that. I believe that you would need to create a bespoke tool for that. Perhaps MS Access or a web-based app.