Borlaff et al. (2014) found that the characteristic photometric parameters of antitruncated discs in S0 galaxies follow tight scaling relations. Now, we have investigated if these scaling relations are satisfied by Type-III galaxies of other morphological types using published data in the R and Spitzer 3.6 microns bands. We have found that the scaling relations (involving the inner and outer disc scalelengths, their corresponding central surface brightnesses, and break radii) are similar in: 1) both S0's and spirals of all galaxy types from Sa to Scd, 2) both in optical and NIR, and 3) both for barred and non-barred galaxies. Despite the wide diversity of mechanisms that may have triggered the formation of antitruncated stellar discs, the strong structural coupling implied by these scaling relations is evidence for the existence of a basic physical process after their formation in disc galaxies of all Hubble types, unrelated to bars.