I am making a direct (probably free/libre) competitor to a minor element of Microsoft Office which is soon due to cease development.
Can I use a modified version of an existing Microsoft program icon as the icon for my software?
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No, you can not base your icon on another icon that is a clear copyright breach. Being a free software has no bearing on the issue.
See what your trying to do is piggyback on somebody else's work because its already recognized by your potential users. This is exactly the kind of thing copyright is trying to prevent.
You need to do your own icons and do the work of making people familiar with your icon and your tool. Yes this means time and effort need to be used, which is kind of the point.