A well tool with multi-stage remedial system improves the durability of a subterranean well tool having an expanded elastomeric member, such as a packer, for use inside a tubular member. The well tool with multi-stage remedial system has a plurality of mandrel members shiftable within the tubular member for anchoring and for setting the seal system. A floating tandem mounted annularly around the lower mandrel members has one end (upon shifting) proximate an end of the seal system, and the floating tandem has an opening to ambient bottom-hole-pressure of the subterranean well. A locking tandem is interposed with the floating tandem and at least one of the lower mandrel members. The floating tandem and the locking tandem together assist in abating elastomeric member extrusion under high temperature, high pressure environments as well as other conditions lending to failure within the well.