Within the FLASH2020+ upgrade, the pump-probe laser capabilities of the extreme ultraviolet and soft x-ray free-electron laser (XFEL) FLASH in Hamburg will be extended. In particular, providing wavelength tunability, shorter pulse durations, and reduced arrival time jitter will increase the scientific opportunities and the time resolution for the XFEL-optical laser pump-probe experiments. We present here a novel concept for the pump-probe laser at FLASH that is based on the post-compression of picosecond pulses emitted from high-power Ytterbium:YAG slab amplifiers. Flexible reduction of the pulse duration is facilitated by spectral broadening in pressure-tunable multi-pass cells. As an application, we show the pumping of a commercial optical parametric amplifier with 150 fs post-compressed pulses. By means of an additional difference frequency generation stage, tunable spectral coverage from 1.3 to 16 μm is reached with multi-μJ, sub-150 fs pulses. Finally, a modular reconfiguration approach to the optical setups close to the free-electron laser instruments is implemented. This enables fast installation of the nonlinear frequency converters at the end stations for user operation and flexibility between different instruments in the two experimental halls.