The Veranda Main Street addition was anchored by Service Merchandise and the mall's first Last Call from Neiman Marcus location.
Photo from from www.sawgrassmillsmall.com (website on Internet Archive Wayback Machine website)

The Oasis was the first open-air wing at SAWGRASS MILLS. It featured stores and restaurants that were a bit more upscale than those in the original sections of the mall.   
Photo from http://www.panoramio.com / "Andes"