A packer provides multiple seals when deployed downhole. Exposed to an activating agent, a swellable element on the packer's mandrel expands radially outward to form a seal with the borehole wall. One or more deformable elements, such as compressible packers or cup packers, are disposed on the mandrel adjacent the swellable element. These deformable element deform outward to the surrounding borehole wall to at least partially isolate the downhole annulus and the swellable element. Bias units releasably affixed on the tool adjacent the deformable elements can deform the elements. These bias unit can be released either by swelling of the swellable element or by fluid pressure. Once released, the bias units are axially biased toward the deformable elements to deform them. In this way, the packer can form multiple seals with the borehole wall, and the deformable elements can isolate the swellable element from the downhole annulus, which can keep the swellable element from degrading or being overly extruded.