Can you create a new selection list field, Stores_2, or something like that. Then, in the properties for the new Stores_2 selection list, under Text Field Options, select, Input Type = "From Another Field". Click the button that says, "Select Shared Field". Navigate to the Stores field in the Stores table.
You have not only the relationship of Stores >>> has many >>> Projects, but also a second list of Stores in the Projects record coming from the source Stores table in the new drop down selection list. The [Stores_2] list will behave independently and does not mimic the parent Store selection.
Does this adequately address your question?