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Ferroelectric materials directly convert electrical energy to mechanical or thermal work and are critical to applications such as sensors, transducers, actuators, and cooling devices. Numerous efforts have been undertaken to develop materials with high electrocaloric (EC) and electromechanical (EM) responses. Here, we present a theoretical analysis, based on thermodynamic fundamentals, for developing ferroelectric materials with high EC and EM responses, i.e., searching for and operating the material near an invariant critical point (ICP). We show that by tailoring the constraints to maximize the number of coexisting phases near ICPs, large EC and EM responses may be realized.