The combination of tunable direct bandgap III-V absorbers with active Si substrates promises high-efficiency tandem solar cells. To yield the ideal III-V bandgaps between 1.6 and 1.8 eV which is considered to achieve current matching with the Si bottom-cell, however, either a big lattice-mismatch or dilute nitrides had to be considered so far. Here, we propose a new structure for a two-terminal III-V-on-Si solar cell which bases on strain-balanced multi-quantum wells (MQWs) embedded in a metamorphic GaAsP top-cell matrix. Strain balanced MQWs extend the absorption edge to a longer wavelength and enable a reduction of the As content in the GaAsP metamorphic top-cell matrix. And accumulation of carriers in MQWs favors radiative recombination, which is beneficial for high efficiency while deep quantum wells lower the charge carrier collection efficiency. Here, we predict solar energy conversion efficiencies over 42.6% with an entire MQW as thin as 500 nm. The applied model takes into account the drawbacks of MQWs, such as limited light absorption and the bottleneck of charge carrier collection from the confinement.