Context. Gamma-ray burst (GRB) afterglows originate from the interaction between the relativistic ejecta and the surrounding medium. Consequently, their properties depend on several aspects: radiation mechanisms, relativistic shock micro-physics, circumburst environment, and the structure and geometry of the relativistic jet. While the standard afterglow model accounts for the overall spectral and temporal evolution for a number of GRBs, its validity limits emerge when the data set is particularly rich and constraining, especially in the radio band. Aims. We aimed to model the afterglow of the long GRB 160131A (redshift z  = 0.972), for which we collected a rich, broadband, and accurate data set, spanning from 6 × 10 8 Hz to 7 × 10 17 Hz in frequency, and from 330 s to 160 days post-burst in time. Methods. We modelled the spectral and temporal evolution of this GRB afterglow through two approaches: (1) the adoption of empirical functions to model an optical/X-ray data set, later assessing their compatibility with the radio domain; and (2) the inclusion of the entire multi-frequency data set simultaneously through the Python package named S AG A (Software for AfterGlow Analysis), to obtain an exhaustive and self-consistent description of the micro-physics, geometry, and dynamics of the afterglow. Results. From deep broadband analysis (from radio to X-ray frequencies) of the afterglow light curves, GRB 160131A outflow shows evidence of jetted emission. Moreover, we observe dust extinction in the optical spectra, and energy injection in the optical/X-ray data. Finally, radio spectra are characterised by several peaks that could be due to either interstellar scintillation (ISS) effects or a multi-component structure. Conclusions. The inclusion of radio data in the broadband set of GRB 160131A makes a self-consistent modelling barely attainable within the standard model of GRB afterglows.