In the present work, we have synthesized rare-earth ion modified Bi4−xRExTi2Fe0.7Co0.3O12−δ (RE = Dy, Sm, La) multiferroic compounds by the conventional solid-state route. Analysis of X-ray diffraction by Rietveld refinement confirmed the formation of a polycrystalline orthorhombic phase. The morphological features revealed a non-uniform, randomly oriented, plate-like grain structure. The peaks evident in the Raman spectra closely corresponded to those of orthorhombic Aurivillius phases. Dielectric studies and impedance measurements were carried out. Asymmetric complex impedance spectra suggested the relaxation of charge carriers belonging to the non-Debye type and controlled by a thermally activated process. Temperature-dependent AC conductivity data showed a change of slope in the vicinity of the phase transition temperature of both magnetic and electrical coupling natures. Based on the universal law and its exponent nature, one can suppose that the conduction process is governed by a small polaron hopping mechanism but significant distortion of TiO6 octahedral. The doping of the A-sites with rare-earth element ions and changes in the concentrations of Fe and Co ions located on the B-sites manifested themselves in saturated magnetic hysteresis loops, indicating competitive interactions between ferroelectric and canted antiferromagnetic spins. The magnetic order in the samples is attributed to pair-wise interactions between adjacent Fe3+–O–Fe3+, Co2+/3+–O–Co3+/2+, and Co2+/3+–O–Fe3+ ions or Dzyaloshinskii–Moriya interactions among magnetic ions in the adjacent sub-lattices. As a result, enhanced magnetoelectric coefficients of 42.4 mV/cm-Oe, 30.3 mV/cm-Oe, and 21.6 mV/cm-Oe for Bi4−xDyxTi2Fe0.7Co0.3O12−δ (DBTFC), Bi4−xLaxTi2Fe0.7Co0.3O12−δ (LBTFC), and Bi4−xSmxTi2Fe0.7Co0.3O12−δ (SBTFC), respectively, have been obtained at lower magnetic fields (<3 kOe). The strong coupling of the Aurivillius compounds observed in this study is beneficial to future multiferroic applications.