One of the most frequent and severe aftermaths of a stroke is the loss of upper limb functionality. Therapy started in the sub-acute phase proved more effective, mainly when the patient participates actively. Recently, a novel set of rehabilitation and support robotic devices, known as supernumerary robotic limbs, have been introduced. This work investigates how a surface electromyography (sEMG) based control strategy would improve their usability in rehabilitation, limited so far by input interfaces requiring to subjects some level of residual mobility. After briefly introducing the phenomena hindering post-stroke sEMG and its use to control robotic hands, we describe a framework to acquire and interpret muscle signals of the forearm extensors. We applied it to drive a supernumerary robotic limb, the SoftHand-X, to provide Task-Specific Training (TST) in patients with sub-acute stroke. We propose and describe two algorithms to control the opening and closing of the robotic hand, with different levels of user agency and therapist control. We experimentally tested the feasibility of the proposed approach on four patients, followed by a therapist, to check their ability to operate the hand. The promising preliminary results indicate sEMG-based control as a viable solution to extend TST to sub-acute post-stroke patients.