We combine a Ginzburg-Landau model for a ferroelastic transition with the theory of micromagnetism to study the magnetostructural behavior leading to multicaloric effects in ferromagnetic shape memory alloys. We analyze the ferroelastic transition under different conditions of temperature, stress and magnetic field and establish the corresponding phase diagram. On the one hand, our results show that the proper combination of both fields may be used to reduce the transition hysteresis and thus improve the reversibility of the related elastocaloric effects, superelasticity and stress-mediated magnetocaloric effects. On the other hand, the stress-free magnetic field-driven and thermally driven magnetostructural evolution provides physical insight into the low-temperature field-induced domain reorientation, from which we derive strategies to modify the operational temperature ranges and thus the corresponding (magnetic) shape-memory effect.