Glycolonitrile, the product of combining CH2O and HCN, is an intermediate in the Strecker reaction leading to the synthesis of the amino acid glycine. However, besides glycine, a plethora of other compounds are also generated when CH2O and HCN react in the presence of ammonia and water. As a starting point to analyze the possible components of this complex mixture, we have employed density functional theory to construct a free energy map of all two-carbon (C2) species that may be present when glycolonitrile participates in addition or elimination reactions with ammonia and water. By identifying thermodynamic sinks and kinetic barriers, we find that the myriad C2 species can be grouped into three broad regions across the free energy landscape. This allows us to trace possible routes to glycine and other molecules of interest in the reaction mixture. The present map also extends our previous work on one-carbon (C1) species. We had previously found one issue with our computational protocol in the C1 map; however, our present C2 map provides a larger data set that supports using an empirical correction to our original protocol for imidic acid to amide transformations, without increasing the computational cost, while retaining the original protocol for other classes of reactions.