We calculate the conductances and the tunneling magnetoresistance (TMR) of double magnetic tunnel junctions, taking as a model example junctions composed of Fe/ZnSe/Fe/ZnSe/Fe (001). The calculations are done as a function of the gate voltage applied to the in-between Fe layer slab. We find that the application of a gate voltage to the in-between Fe slab strongly affects the junctions TMR due to the tuning or untuning of conductance resonances mediated by quantum well states. The gate voltage allows a significant enhancement of the TMR, in a more controllable way than by changing the thickness of the in-between Fe slab. This effect may be useful in the design of future spintronic devices based on the TMR effect, requiring large and controllable TMR values.