ABSTRACT AQ Men is a nova-like variable that is presumed to have a tilted, precessing accretion disc. Grazing eclipses in this system have been speculated to be useful in exploring the geometry of its accretion disc. In this work, we analysed Transiting Exoplanet Survey Satellite (TESS) observations of AQ Men, which provide the best light curve of this object thus far. We show that the depths of the eclipses are changing with the orientation of the accretion disc, which means that they can serve as a direct test of the tilted accretion disc models. The precession period of the accretion disc is increasing during the TESS observations. However, it is still shorter than the period determined in the previous studies. The amplitude of the variability related to the precession of the accretion disc varies, and so does the shape of this variability. Moreover, we have detected a positive superhump that was previously unseen in AQ Men. Interestingly, the positive superhump has a strongly non-sinusoidal shape, which is not expected for a nova-like variable.