A multistimuli response to temperature and pressure is found in the hybrid inorganic-organic perovskite-like [TPrA][Mn(dca)3] compound, which is related to a first-order structural phase transition near room temperature, Tt ≈ 330 K. This phase transition involves a transformation from room temperature polymorph I, with the noncentrosymmetric space group P4̅21c, to the high temperature polymorph II, with the centrosymmetric space group I4/mcm, and it implies ionic displacements, order-disorder phenomena, and a large and anisotropic thermal expansion (specially along the c-axis). As a consequence, [TPrA][Mn(dca)3] exhibits a dielectric anomaly, associated with the change from a cooperative to a noncooperative electric behavior (antiferroelectric (AFE)-paraelectric (PE) transition). The former implies an AFE distribution of electric dipoles in polymorph I, related to the described off-shift of the apolar TPrA cations and the order-disorder of the polar dca ligands mechanisms, that are different from those reported, up to now, for others perovskite-type hybrid compounds. Such cooperative electric order, below Tt ≈ 330 K, coexisting with long-range antiferromagnetic ordering below T = 2.1 K render the [TPrA][Mn(dca)3] a new type-I multiferroic material. In addition, the obtained experimental results reveal that this compound is also a multistimuli-responsive material, with a very large sensitivity toward temperature and applied external pressure, δTt/δP ≈ 24 K kbar(-1), even for small values of pressure (P < 2 kbar). Therefore, this material opens up a potential interest for future technological applications, such as temperature/pressure sensing.