We have deposited polycrystalline Re-doped (Fe65Co35)(100−x)Rex (0≤x≤12.6 at. %) thin films grown under identical conditions and sandwiched between thin layers of Ru in order to study the phenomenon of spin pumping as a function of Re concentration. In-plane and out-of-plane ferromagnetic resonance spectroscopy results show an enhancement of the Gilbert damping with an increase in Re doping. We find 98% enhancement in the real part of effective spin mixing conductance Re(geff↑↓) with Re doping. Conversely, the Re(geff↑↓) does not change with Re doping in Fe65Co35 thin films which are seeded and capped with Cu layers. The enhancement in Re(geff↑↓) of Re-doped Fe65Co35 thin films sandwiched between thin layers of Ru is linked to the Re doping-induced change of the interface electronic structure in the nonmagnetic Ru layer. The saturation magnetization decreases 35% with increasing Re doping up to 12.6 at. %. This study opens a direction of tuning the spin mixing conductance in magnetic heterostructures by doping of the ferromagnetic layer, which is essential for the realization of energy-efficient operation of spintronic devices.