Robot-Assisted Therapy (RAT) has successfully been used to improve social skills in children with autism spectrum disorders (ASD) through remote control of the robot in so-called Wizard of Oz (WoZ) paradigms. However, there is a need to increase the autonomy of the robot both to lighten the burden on human therapists (who have to remain in control and, importantly, supervise the robot) and to provide a consistent therapeutic experience. This paper seeks to provide insight into increasing the autonomy level of social robots in therapy to move beyond WoZ. With the final aim of improved human-human social interaction for the children, this multidisciplinary research seeks to facilitate the use of social robots as tools in clinical situations by addressing the challenge of increasing robot autonomy. We introduce the clinical framework in which the developments are tested, alongside initial data obtained from patients in a first phase of the project using a WoZ set-up mimicking the targeted supervised-autonomy behaviour. We further describe the implemented system architecture capable of providing the robot with supervised autonomy.