The efficiency limit of an intermediate band (IB) solar cell can be increased by a "tandem" configuration of multiple intermediate band devices. Thermodynamic models show that the efficiency of a two-stack tandem of IB devices achieves the efficiency of a six junction series connected solar cell. The efficiency of an IB in conjunction with a single or double stack tandem has similar efficiency advantages. Further, analysis of the materials which can be used to implement IB solar cells in a tandem configuration shows advantages relating to the ability to implement IB materials with quantum wells or quantum dots. For a single IB solar cell, a key difficulty is identifying materials for the barrier and the quantum well which have a small valence band offset and large conduction band offset (or the reverse). The use of an IB solar cell as the bottom solar cell of a tandem allows a larger range of materials with suitable barrier band gaps and a smaller ideal conduction band offset. A further theoretical advantage of such a structure is that it avoids the extremely low open circuit voltages achieved from pn junctions in low bandgap materials; for example, the thermodynamic optimum for a 6 junction tandem solar cell has its lowest bandgap below 0.4 eV. We present a thermodynamic model for IB hybrid tandem configurations which does not assume spectral selectivity among the different solar cells and predicts that a barrier/quantum dot structure can have an efficiency as high as 60 to 70 percent at 1X blackbody radiation.