Resistive switching in multiferroics has attracted increasing attention due to the potential application for next-generation nonvolatile memory and could lead to forms of computing. However, the resistive switching mechanism in solid solution oxides is unclear. In this article, we have successfully fabricated binary 0.72BiTi0.27Fe0.46Mg0.27O3-0.28LaFeO3 (BTFM-LFO) and ternary 0.625BiTi0.27Fe0.46Mg0.27O3-0.25LaFeO3-0.125La2MgTiO6 (BTFM-LFO-LMT) thin films with precise component control by the spin coating method. The solid solution films exhibit obvious ferroelectricity and magnetism at room temperature. Both binary and ternary solid solution films show switchable polarization, weak magnetism, and reversible and repeatable resistive switching effects. Multistage resistive switching behavior was observed. Four resistive switching states were obtained in the binary film; the highest Ion/off is up to 106. The influence of the film composition on the resistive switching effect was discussed. It is considered that the oxide vacancy/valance exchange-induced defects play a dominant role in the resistive switching effect of complex oxide thin films. This work provides an alternative pathway to explore the resistive switching in multiferroic oxides by fabrication of complex solid solution films.