It's possible that what you need here is a join table to facilitate a many to many relationship. A product can be available at multiple locations and a location can list multiple products. Assuming that you need to record more info than just the name (and maybe an ID) in the location table...
Start with these relationships:
Products::__pkProductID = Product_Location::_fkProductID
Locations::__pkLocationID = Product_Location::_fkLocationID
You can place a portal to Product_Location on the Products layout to list and select Locations records for each given Products record. Fields from Locations can be included in the Portal to show additional info about each selected Locations record and the _fkLocationID field can be set up with a value list for selecting Locations records by their ID field.
With such a set up, it is then possible to set up a portal to an additional Tutorial: What are Table Occurrences? of Locations with buttons that select/deselect a location by adding or deleting records from Product_Location--just like a check box. Conditional formatting (and possibly FMP 13's new "hide object when" property) can make this button look and change appearance just like a check box.
This demo file has an example layout that uses this method: https://www.dropbox.com/s/oyir7cs0yxmbn6i/ManyToManywDemoWExtras.fp7