We have presented here developments to the ChemDASH methodology allowing for the consideration of magnetic structures and the variation of the composition of a system during a ChemDASH run. We show that the original ChemDASH methodology is an efficient search algorithm for finding low energy configurations of spinels in the Mn-Fe-Zn-O phase field. From this, we show that the new variable composition methodology can be used to assess the likelihood that a solid solution forms between two end members without having to assess all compositions individually. By reducing the number of structures that need to be assessed, this methodology provides an efficient search in both composition and chemical space. We also show that this methodology works well with different magnetic structures and starting configurations ideal for evaluating unknown composition spaces in solid solutions between materials. It is envisaged that this methodology will be used to evaluate solid solutions in other structure types (e.g. perovskites) beyond spinels to find new materials with functional properties.