Context. It has been recently found that the characteristic photometric parameters of anti-truncated discs in S0 galaxies follow tight scaling relations. Aims: We investigate whether similar scaling relations are satisfied by galaxies of other morphological types. Methods: We have analysed the trends in several photometric planes relating the characteristic surface brightness and scalelengths of the breaks and the inner and outer discs of local anti-truncated S0-Scd galaxies, using published data and fits performed to the surface brightness profiles of two samples of Type-III galaxies in the R and Spitzer 3.6 μm bands. We have performed linear fits to the correlations followed by different galaxy types in each plane, as well as several statistical tests to determine their significance. Results: We have found that 1) the anti-truncated discs of all galaxy types from Sa to Scd obey tight scaling relations both in R and 3.6 μm, as observed in S0s; 2) the majority of these correlations are significant accounting for the numbers of the available data samples; 3) the trends are clearly linear when the characteristic scalelengths are plotted on a logarithmic scale; and 4) the correlations relating the characteristic surface brightnesses of the inner and outer discs and the breaks with the various characteristic scalelengths significantly improve when the scalelengths are normalized to the optical radius of the galaxy. The observational uncertainties prevent us from discerning robustly whether the trends differ between the different types and bands, but we do not find statistical evidence of significant differences between the distributions of S0s and spirals or of barred and unbarred galaxies. These results suggest that the scaling relations of Type-III discs are independent of the morphological type and the presence (or absence) of bars within the observational uncertainties of the available datasets. However, larger and deeper samples are required to confirm this. Conclusions: The tight structural coupling implied by these scaling relations imposes strong constraints on the mechanisms proposed to explain the formation of anti-truncated stellar discs in the galaxies across the whole Hubble sequence. Tables 2-7 are available in electronic form at http://www.aanda.org