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We investigate possible evidence from Extended Theories of Electro-Magnetismby looking for deviations from the Amp\`ere-Maxwell law. The photon, mainmessenger for interpreting the universe, is the only free massless particle inthe Standard-Model (SM). Indeed, the deviations may be due to a photon mass forthe de Broglie-Proca (dBP) theory or the Lorentz-Poincar\'e Symmetry Violation(LSV) in the SM Extension (SME), but also to non-linearities from theories asof Born-Infeld, Heisenberg-Euler. With this aim, we have analysed six years ofdata of the Magnetospheric Multi-Scale mission, which is a four-satelliteconstellation, crossing mostly turbulent regions of magnetic reconnection andcollecting about 95\% of the downloaded data, outside the solar wind. Weexamined 3.8 million data points from the solar wind, magnetosheath, andmagnetosphere regions. In a minority of cases, for the highest time resolutionburst data and optimal tetrahedron configurations drawn by the four spacecraft,deviations have been found ($2.2\%$ in modulus and $4.8\%$ in Cartesiancomponents 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 extremelow-mass range). The deviations might be due to unaccounted experimental errorsor, less likely, to non-Maxwellian contributions, for which we have inferredthe related parameters for the dBP and SME cases. Possibly, we are at theboundaries of measurability for non-dedicated missions. We discuss ourexperimental 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-dependentlimits.

Testing the Amp\`ere-Maxwell law on the photon mass and Lorentz-Poincar\'e symmetry violation with MMS multi-spacecraft data