The word symbiosis (Merriam-Webster 2015) has its origins in biology where it means "the relationship between two different kinds of living things that live together and depend on each other." When referring to symbiotic cognitive computing, we expand this definition to include both people and intelligent computational agents who work together in a partnership (Farrell et. al 2005). Cognitive objects embody these intelligent agents, providing a physical object that may sense, compute, react, and interact with the power of cognitive computing. In this paper, we describe a few preliminary design explorations that investigate the impact of being surrounded by cognitive objects during group meetings. We frame a research agenda around the construction, programming, and usage of cognitive objects in work and home environments, and for use cases across industries such as oil and gas, healthcare and agriculture.