This clinical trial evaluates two surgical techniques (targeted muscle re-innervation \[TMR\] and regenerative peripheral nerve interfaces \[RPNI\]) alone and in combination for the alleviation of chronic residual limb and phantom limb pain in cancer patients who have had an amputation. Chronic residual limb pain and phantom limb pain are debilitating outcomes of traumatic and oncologic amputation. Emerging microsurgical treatments for post-amputation pain are very promising. TMR and RPNI are both approved surgical techniques that involve connecting cut nerves to parts of the muscle as a way to heal and protect the nerves. This trial evaluates these techniques alone and in combination for the treatment of residual and phantom limb pain in cancer patients who have received an amputation.