If you store the file on a shared network drive that others can access you can then send them a shortcut to the file. Excel 2013 has a share workbook option on the review tab that will allow users to make simultaneous edits.
However, 'share workbook' comes with its own limitations (such as not being able to use Tables for starters) and can sometimes be quite prone to file corruption.
If you're ok with the restrictions on it (list here ) then I'd say continue using it but take regular back-ups.
Alternatively, if appropriate for your data set, you could try to departmentalize by having several different files for different people/departments that then all pool data into one master file.
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