Something of the sort already exists: you can have alternate pin names within a symbol. If you open Symbol Editor and double click on a pin (or press E with a pin selected) you can hit the drop down arrow for Alternate Pin Definitions and add as many as you like.
When the symbol is placed in schematic, you can hit E with a symbol selected to open Symbol Properties and edit the “Alternate Pin Assignments” in the tab next to General. It isn’t obvious, but the Alternate Assignment column has a bunch of drop down menus that need to be selected from.
Edit: See Alternate pin assignment - #6 by roboya for nice screenshots