Co-design practices have been used for decades to support participatory engagement in design work. However, despite a wide range of materials that describe the design and commitments of numerous co-design experiences, few descriptions of the knowledge that guides designers when creating these experiences exist. Thus, we ask: What kind of knowledge do designers need to design co-design experiences? What form(s) could intermediate-level knowledge for co-design take? To answer these questions, we adopted a co/auto-ethnographic and Research-through-Design approach to reflexively engage with our design decisions, outcomes, and challenges related to two virtual co-design workshops. We constructed a set of four multi-dimensional facets(Rhythms of Engagement, Material Engagement, Ludic Engagement, and Conceptual Achievement) and three roles (designer, researcher, facilitator) to consider when creating co-design experiences. We illustrate these facets and roles through examples, building new \textit{intermediate-level knowledge} to support future co-design research and design, framing co-design as a designerly practice.