AX J1745.6-2901 is a high-inclination (eclipsing) transient neutron star (NS) low-mass X-ray binary showcasing intense ionized Fe K absorption. We present here the analysis of 11 XMM-Newton and 15 NuSTAR new data sets (obtained between 2013 and 2016), therefore tripling the number of observations of AX J1745.6-2901 in outburst. Thanks to simultaneous XMM-Newton and NuSTAR spectra, we greatly improve on the fitting of the X-ray continuum. During the soft state, the emission can be described by a disc blackbody (kT ∼ 1.1-1.2 keV and inner disc radius rDBB ∼ 14 km), plus hot (kT ∼ 2.2-3.0 keV) blackbody radiation with a small emitting radius (rBB ∼ 0.5 - 0.8 km) likely associated with the boundary layer or NS surface, plus a faint Comptonization component. Imprinted on the spectra are clear absorption features created by both neutral and ionized matter. Additionally, positive residuals suggestive of an emission Fe K α disc line and consistent with relativistic ionized reflection are present during the soft state, while such residuals are not significant during the hard state. The hard-state spectra are characterized by a hard (Γ ∼ 1.9-2.1) power law, showing no evidence for a high energy cut-off (kTe > 60-140 keV) and implying a small optical depth (τ < 1.6). The new observations confirm the previously witnessed trend of exhibiting strong Fe K absorption in the soft state that significantly weakens during the hard state. Optical (GROND) and radio (GMRT) observations suggest for AX J1745.6-2901 a standard broad-band spectral energy distribution as typically observed in accreting NSs.