Neutron-diffraction and magnetization measurements have been carried out on a series of samples of the magnetorefrigerant ${\text{Mn}}_{1+y}{\text{Fe}}_{1\ensuremath{-}y}{\text{P}}_{1\ensuremath{-}x}{\text{Ge}}_{x}$. The data reveal that the ferromagnetic and paramagnetic phases correspond to two very distinct crystal structures, with the magnetic-entropy change as a function of magnetic field or temperature being directly controlled by the phase fraction of this first-order transition. By tuning the physical properties of this system we have achieved a magnetic-entropy change [magnetocaloric effect (MCE)] for the composition ${\text{Mn}}_{1.1}{\text{Fe}}_{0.9}{\text{P}}_{0.80}{\text{Ge}}_{0.20}$ that has a similar shape for both increasing and decreasing field, with the maximum MCE exceeding $74\text{ }\text{J}/\text{kg}\text{ }\text{K}$---substantially higher than the previous record. The diffraction results also reveal that there is a substantial variation in the Ge content in the samples which causes a distribution of transition temperatures that reduces the MCE. It therefore should be possible to improve the MCE to exceed $100\text{ }\text{J}/\text{kg}\text{ }\text{K}$ under optimal conditions.