A group of five perovskite-type ceramic systems was designed by solid-state reaction, increasing the configurational entropy, ΔSconf at the B-site, going from low and medium to finally reaching a high-entropy system. Chemical elements, crystal structure, and microstructure characterization, as well as the dielectric and magnetic properties, are discussed from the single phase LaCrO3 towards a continuous equiatomic multicomponent LaCr0.2Mn0.2Fe0.2Al0.2Ga0.2O3 ceramic compounds. Through a combination of structural analysis and XPS spectroscopy study, it is found that not only the configurational entropy ∆Sconf term, but also the enthalpy of mixing, ΔHmix through of arising of the coexistence of mixed valence state, oxygen vacancies, and local octahedral distortions lead to the stabilization of the single phase in equimolar multicomponent perovskite systems. The arising of Cr3+/Cr6+ and Mn3+/Mn2+ mixed valence state drives the AC electric conductivity through the presence of two kinds of charge carriers, small polarons and oxygen vacancies in LCM, LCMF, LCMFA, and LCMFAG ceramic compounds. The occurrence of these two classes of charge carriers progressively increases the AC electric conductivity at room and high temperatures for each ceramic compound, being higher for the LCMFA entropy compound, making it a potential candidate for solid oxide fuel cell (SOFC) applications. As expected, the increases of compositional random cations display rich magnetic properties arising from competing magnetic interactions driven by the sublattice of Cr, Mn, and Fe magnetic ions. The resulting ΔSconf increase leads to a Griffith-like phase. The results also show that not only the ferromagnetic clusters of the LaMnO3 (AxFz) sublattice but also the weak ferromagnetism associated with the LaCrO3 (GxFz), and LaFeO3 (GxFz) sublattices play a predominant role in the formation of the Griffiths-like phase in the low, medium and high-entropy ceramic systems.