  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 (650-900 nm) and mid-IR (5-20 $\mu$m) 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
mid-IR pump, optical push and broadband probe in a single-crystal of
Bi$_2$Sr$_2$Y$_{0.08}$Ca$_{0.92}$Cu$_2$O$_{8+\delta}$ across the
superconducting and pseudogap phases.
