A multiple layer mattress system is disclosed which addresses the issue of degradation of the elasticity of a foam mattress core. In one embodiment, the multiple layer mattress is formed with split layers; namely, one or more comfort layers and one or more support layers. Each layer is encased with an encasement which includes complementary chiral zippers to enable the comfort layer and the support layer to be removably secured together. The chiral zippers allow the various layers to be rotated 180° relative to each other and reconnected thereto. Layers can also be added to the mattress or replaced to suit a user's comfort level. Optionally, a separate cover may be selectively secured to the top of a comfort layer and/or the bottom of the support layer for accessories. The optional bottom accessory cover may be used to provide active or passive maneuvering of the support layer relative to a foundation. The optional top accessory layer may provide for various accessories including: a protective cover; a heating pad, a smart tech cover, for example, as illustrated at lunasleep.com; a launderable cover; a pillow top and other accessories. An aftermarket mattress encasement is also disclosed that includes a top cover and a bottom cover connectable together by way of a chiral zipper system that allows accessories to be secured on top of a conventional mattress.