Non-standard fields are assumed to be responsible for phenomena attributed to dark energy and dark matter. Being coupled to ordinary matter, these fields modify the masses and/or charges of the elementary particles, thereby violating the weak equivalence principle. Thus, values of fundamental constants such as the proton-to-electron mass ratio, μ, and/or the fine structure constant, α, measured in different environment conditions can be used as probes for this coupling. Here we perform differential measurements of F = μα2 to test a non-standard coupling in the Magellanic Clouds–dwarf galaxies where the overall mass budget is dominated by dark matter. The analysis is based on [C i ] and CO lines observed with the Herschel Space Observatory. Since these lines have different sensitivities to changes in μ and α, the combined α and μ variations can be evaluated through the radial velocity offsets, Δ V , between the CO and [C i ] lines. Averaging over nine positions in the Magellanic Clouds, we obtain 〈Δ V 〉 = −0.02 ± 0.07 km s−1, leading to |Δ F / F | < 2 × 10−7 (1σ), where Δ F / F = (F obs − F lab)/ F lab. However, for one position observed with five times higher spectral resolution we find Δ V = −0.05 ± 0.02 km s−1, resulting in Δ F / F = (−1.7 ± 0.7) × 10−7. Whether this offset is due to changes in the fundamental constants, due to chemical segregation in the emitting gas, or merely due to Doppler noise requires further investigations. [ABSTRACT FROM AUTHOR]