Advanced concept or third generation solar cells rely on modification to the basic process of absorption/recombination or collection to increase the efficiency above that from a singe junction solar cell. While there are a number of advanced concept approaches, a feature of theses is that they have focused primarily on inclusion of a single type of physical mechanism. Such single mechanism advanced concept solar cells are in general limited in efficiency to the equivalent tandem solar cell which has the same number of processes. This paper demonstrates that solar cells using combinations of different approaches have higher thermodynamic efficiencies. Some combinations demonstrate higher efficiencies that either of the constituent approaches, and, significantly, even exceed the efficiency of the "equivalent" tandem structure. Moreover, such advanced concept hybrid structures have benefits other than efficiency increases, including reduced sensitivity to materials or to physical processes which are difficult to implement, or to non-idealities in the solar cell structure.