  We investigate possible evidence from Extended Theories of Electro-Magnetism
by looking for deviations from the Amp\`ere-Maxwell law. The photon, main
messenger for interpreting the universe, is the only free massless particle in
the Standard-Model (SM). Indeed, the deviations may be due to a photon mass for
the de Broglie-Proca (dBP) theory or the Lorentz Symmetry Violation (LSV) in
the SM Extension (SME), but also to non-linearities from theories as of
Born-Infeld, Heisenberg-Euler. With this aim, we have analysed six years of
data of the Magnetospheric Multi-Scale mission, which is a four-satellite
constellation, crossing mostly turbulent regions of magnetic reconnection and
collecting about $95\%$ of the downloaded data, outside the solar wind. We
examined 3.8 million data points from the solar wind, magnetosheath, and
magnetosphere regions. In a minority of cases, for the highest time resolution
burst data and optimal tetrahedron configurations drawn by the four spacecraft,
deviations have been found ($2.2\%$ in modulus and $4.8\%$ in Cartesian
components for all regions, but raising up in the solar wind alone to $20.8\%$
in modulus and $29.7\%$ in Cartesian components and up to 45.2\% in the extreme
low-mass range). The deviations might be due to unaccounted experimental errors
or, less likely, to non-Maxwellian contributions, for which we have inferred
the related parameters for the dBP and SME cases. Possibly, we are at the
boundaries of measurability for non-dedicated missions. We discuss our
experimental results (upper limit of photon mass of $2.1 \times 10^{-51}$ kg,
and of the LSV parameter $|\vec{k}^{\rm AF}|$ of $6 \times 10^{-9}$ m$^{-1}$),
as the deviations in the solar wind, versus more stringent but model-dependent
limits.
