<p>This study primarily investigates the thermo-electro-magneto-mechanical free vibration characteristics of sandwich plates with a core layer made of graphene oxide powder-reinforced nanocomposite (GOPRC) and two outer face sheets composed of magneto-electro-elastic functionally graded materials (PoFGMEE). For convenience, this structure is referred to as PoFGMEE-GOP. The plate is considered to be supported by a three-parameter Kerr elastic foundation. The magneto-electro-elastic properties of the face sheets vary through the thickness following a modified power-law rule that accounts for both even and uneven porosities, while the GOPRC core’s material properties are determined using the Halpin–Tsai model. The magnetic and electric potentials within the PoFGMEE layer are modeled as a blend of cosine and linear functions through its thickness. Additionally, three types of temperature distributions along the plate thickness—uniform, linear, and nonlinear—are also considered. To perform this analysis, a novel model using a four-variable refined plate theory (HSDT-4), combined with the pb2-Ritz method, is developed. Comparative examples validate the accuracy of the model. New numerical findings are provided to assess the influence of temperature, magnetic potential, electric voltage, power-law index, porosity distribution type, porosity coefficient, graphene oxide powder distribution type, thickness ratio of the core to the face sheet, and foundation elasticity on the free vibration response of PoFGMEE-GOP sandwich plates.</p>