May-Cohens morphed into a May Company Florida before being converted to a Baton Rouge-based Maison Blanche. That store was rebranded by Mobile-based Gayfer's. It became part of a Dillard's "Triple-header" in 1998. This was, apparently, the second time that Dillard's operated three stores simultaneously in one mall (the first Triple-header had been set up in 1992, at Greater Cleveland's WESTGATE MALL).    
Photo from http://www.bing.com

Graphic from May Department Stores Company