Medical implants are commonly made of biocompatible metals such as titanium, which is known to promote cell adhesion on its surface. Recent advancements in additive manufacturing have made the tailored 3D-printing of titanium implants more attractive than ever, due to the possibility to reduce weight and increase structural complexity. It has been demonstrated that osseointegration can be enhanced even further if the implant presents a surface roughness in the micro- and sub-micrometer scale. In this work, we explore the potential of Direct Laser Interference Patterning (DLIP) for the fabrication of complex multiscale periodic micro- and nanostructures on an additively manufactured Ti-13Nb-13Zr alloy. A picosecond pulsed laser with a two-beam DLIP configuration is used to manufacture line-like microstructures in a single processing step with up to four levels of hierarchy. Process parameters, such as the period of the line-like pattern, the laser wavelength, the pulse-to-pulse overlap and the laser fluence, have been varied throughout the experiments. As a result of the ultra-short pulse laser radiation, laser-induced periodic surface structures (LIPSS) have been generated and these occur in the form of high spatial frequency LIPSS (HSFL), low spatial frequency LIPSS (LSFL) and supra-wavelength grooves, producing periods from 83 nm to 3.1 µm. Furthermore, we show that the period of the different scale features can be tuned by varying different process parameters. In fact, while the period of LSFL and HSFL is shown to depend on the choice of wavelength, the period of the grooves depends linearly on the cumulated laser fluence used for the fabrication. On the contrary, the DLIP period can be deterministically controlled through the arrangement of the interference optics. The obtained four-level hierarchical structures may show great potential as an approach to enhance osseointegration in the next generation of medical implants.