The limiting efficiency of a solar cell enhanced by both up- and downconversion is calculated to be 44.6% under one sun illumination using a detailed balance formalism. We show that solar cells are enhanced by both spectral conversion and photon recycling. This device architecture has the advantage of being able to enhance existing technologies after relatively few modifications. Importantly, we show that this device architecture's limiting efficiency peaks close to the band gap of silicon, unlike other spectral converters with three absorbing thresholds.