Storytelling plays a central role in human socializing and entertainment, and research on conducting storytelling with robots is gaining interest. However, much of this research assumes that story content is curated. In this paper, we expand the recently-proposed task of collaborative storytelling, where an intelligent agent and a person collaborate to create a unique story by taking turns adding to it, for application to social robot and consider the design implications that arise. Since latency can be detrimental to human-robot interaction, we examine the performance-latency trade-offs of an existing generate-and-rank-based approach to collaborative storytelling by finding the optimal ranker’s sample size that strikes the best balance between quality and computational cost. We improve on existing evaluation that was previously based on system-generated stories by having human participants play the collaborative storytelling game with our system and comparing the stories they create with our system to a naive baseline. Finally, we conduct a pilot elicitation survey that sheds light on issues to consider when adapting our collaborative storytelling system to a social robot. Our evaluation shows that participants have a positive view of collaborative storytelling with a social robot and consider rich, emoting capabilities to be key to enjoyment.