The new xMnAs/(1 − x)PMN–PT (x = 0.2, 0.3) multicaloric composites, consisting of the modified PMN–PT-based relaxor-type ferroelectric ceramics and ferromagnetic compound of MnAs were fabricated, and their structure, magnetic, dielectric properties, and caloric effects were studied. Both components of the multicaloric composite have phase transition temperatures around 315 K, and large electrocaloric (~0.27 K at 20 kV/cm) and magnetocaloric (~13 K at 5 T) effects around this temperature were observed. As expected, composite samples exhibit a decrease in magnetocaloric effect (<1.4 K at 4 T) in comparison with an initial MnAs magnetic component (6.7 K at 4 T), but some interesting phenomena associated with magnetoelectric interaction between ferromagnetic and ferroelectric components were observed. Thus, a composite with x = 0.2 exhibits a double maximum in isothermal magnetic entropy changes, while a composite with x = 0.3 demonstrates behavior more similar to MnAs. Based on the results of experiments, the model of the multicaloric effect in an MnAs/PMN–PT composite was developed and different scenario observations of multicaloric response were modeled. In the framework of the proposed model, it was shown that boosting of caloric effect could be achieved by (1) compilation of ferromagnetic and ferroelectric components with large caloric effects in selected mass ratio and phase transition temperature; and (2) choosing of magnetic and electric field coapplying protocol. The 0.3MnAs/0.7PMN–PT composite was concluded to be the optimal multicaloric composite and a phase shift ∆φ = −π/4 between applied manetic fields can provide a synergetic caloric effect at a working point of 316 K.