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In general, the constituents of the bulk matter produced in heavy-ion collisions carry, besides electric charge, multiple other conserved quantum numbers like baryon number and strangeness. Therefore, an electric field will not only generate an electric current but, at the same time, also currents in baryon number and strangeness. We propose that the impact of the electric field on these conserved currents should be characterized by additional transport coefficients, which we call cross-conductivities. In this paper, we introduce and present a calculation of these cross-conductivities from the Green-Kubo formalism within the transport code SMASH for different chemical compositions of hadron resonance gases. We find that the coefficients underlie an ordering in the active degrees of freedom and that thus the chemical composition of the system plays a crucial role. Further, we argue that in future comparisons of lattice QCD calculations with these findings, one could constrain which degrees of freedom and their corresponding charge properties are relevant for the QCD dynamics of the system.