Socially Assistive Robotics (SAR) has increasingly been shown to have potential as a tool for social skills therapy for children with Autism Spectrum Disorder (ASD), a developmental disorder associated with difficulties in social functioning. This work suggests that the broad appeal of SAR systems to children with ASD is due to robots’ ability to be interpreted in agent-like and object-like ways. We describe the development of a SAR interaction scenario with both agent-like and object-like robot behaviors, and present the results of a pilot study of six children with ASD interacting with a humanoid robot with the full controller, as well as three types of control: a non-humanoid “box” robot with similar behavior (reduced morphological agency), a humanoid robot with random behavior (reduced behavioral agency), and a robotic toy (reduced morphological and behavioral agency). We show that across these multiple levels and types of agency of the interaction partner, children can be classified into two groups: 1) those with more object-like interactions with the robot, and 2) those with more agent-like interactions. Participants in each group show consistent patterns of behavior across several outcome measures consistent with the agency-based interpretation of the groups, including vocalizations, head orientation to the robot’s head, and button-pressing behavior. Harnessing this flexibility of the robot’s role can scaffold children towards more frequent positive social interactions with other people, while maintaining an enjoyable and engaging interaction.