The NA64 experiment at the CERN SPS has obtained the world-leading constraints in the search for Light Dark Matter (LDM) candidates with sub-GeV masses using an electron beam. Most recently, the complementarity of the physics case with the NA64$e^{+}$ and NA64$\mu$ programs has been established, in particular following the first results for searches with high-energy muons. Planned upgrades for all programs during the CERN's next long shutdown (LS3) are aimed at boosting the experiment data-taking capabilities and ensuring a low level of background, further enhancing the sensitivity to the uncharted region of the parameter space suggested by benchmark LDM models. Finally, the feasibility of Dark Sector (DS) searches with hadronic beams, NA64$h$, has been demonstrated, opening a new avenue for exploration.