Solid-state cooling applications based on electrocaloric (EC) effects are particularly promising from a technological point of view due to their downsize scalability and natural implementation in circuitry. However, EC effects typically involve materials that contain toxic substances and require relatively large electric fields (∼100-1000 kV cm-1) that cause fateful leakage current and dielectric loss problems. Here, we propose a possible solution to these practical issues that consists of concertedly applying hydrostatic pressure and electric fields on lead-free multiferroic materials. We theoretically demonstrate this strategy by performing first-principles simulations on supertetragonal BiFe1-xCoxO3 solid solutions (BFCO). It is shown that hydrostatic pressure, besides adjusting the occurrence of EC effects to near room temperature, can reduce enormously the intensity of driving electric fields. For pressurized BFCO, we estimate a colossal room-temperature EC strength, defined as the ratio of the adiabatic EC temperature change by an applied electric field, of ∼1 K cm kV-1, a value that is several orders of magnitude larger than those routinely measured in uncompressed ferroelectrics.