Governments are increasing reaching out beyond their organizational boundaries to engage citizens in policy design, co-created and co-delivered public services. While social media platforms have been largely used by government entities for communicating with and obtaining feedbacks on programs and services from citizens; traditional websites remain the primary interaction channel for emerging co-delivered services involving Citizen-to-Government (C2G) interactions. This work explores the affordances of the social media platform as a more natural platform to support not only C2G, but also Citizen-to-Citizen services (C2C) and Intermediary-to-Government (I2G) services. By considering a set of concrete C2C and C2G initiatives, we determine 1) the extent to which social media platform affordances support these initiatives, 2) the relative advantage of using these social media platforms over traditional government websites. Insights from this work should help in moving Government Social Media policies to cover the use of social media channels for C2C, C2G and I2G services.