  We use a specific form of the interpolation function in the MOND formalism,
which optimally accounts for the internal structure of dwarf spheroidal (dSph)
galaxies, to explore the consequences it has on the scaling relations seen in
these systems.}} {{The particular form of the interpolation function we used
leads to a law of gravity that does not degrade the good fit of the MOND
proposal on galactic scales, and in fact, slightly improves the accordance with
observations at dSph scales. This formalism yields a good description of
gravitational phenomena without the need of invoking any still undetected and
hypothetically dominant dark matter, in the weak field regime probed by local
dSph galaxies.}} {{Isothermal equilibrium density profiles then yield projected
surface density profiles for the local dSph galaxies in very good agreement
with observational determinations, for values of the relevant parameters as
inferred from recent observations of these Galactic satellites. The observed
scaling relations for these systems are also naturally accounted for within the
proposed scheme, including a previously unrecognised correlation of the
inferred mass-to-light ratios of local dSph's with the ages of their stellar
populations, which is natural in modified gravity schemes in the absence of
dark matter.}} {The results shed some light on the form that the MOND
interpolating function may have in the most challenging regime, which occurs at
moderate accelerations and intermediate mass--weighted lengths.
