We report here an experimental setup to perform three-pulse pump-probe measurements over a wide wavelength and temperature range. By combining two pump pulses in the visible (650 nm-900 nm) and mid-IR (5 μm-20 μm) range, with a broadband supercontinuum white-light probe, our apparatus enables both the combined selective excitation of different material degrees of freedom and a full time-dependent reconstruction of the non-equilibrium dielectric function of the sample. We describe here the optical setup, the cryogenic sample environment, and the custom-made acquisition electronics capable of referenced single-pulse detection of broadband spectra at the maximum repetition rate of 50 kHz, achieving a sensitivity of the order of 10-4 over an integration time of 1 s. We demonstrate the performance of the setup by reporting data on a mid-IR pump, optical push, and broadband probe in a single crystal of Bi2Sr2Y0.08Ca0.92Cu2O8+δ across the superconducting and pseudogap phases.