From experiments it is known that magnetostatic interactions between grains strongly affect the magnetic hysteresis behaviour of samples, however, because of the difficulty in predicting the non-linear behaviour, the effect of interactions has not yet been fully incorporated into theoretical models for the recently developed first-order-reversal-curve (FORC) method. For the FORC method to be widely used it is important to have such an understanding, for example, from a geological point of view there are many cases where interactions are known to be important, e.g. bacterial magnetosomes found in sedimentary rocks. Using a 3-D fast-Fourier transforms (FFT) micromagnetic model we have conducted a detailed study of the role of magnetostatic interactions on the FORC diagrams of assemblages of ideal single-domain (SD) magnetite-like grains. We have considered various anisotropies and the importance of the alignment configuration of the particle assemblages. We show that interactions can strongly affect the magnetic behaviour, for example, interacting assemblages of SD grains can display more MD-like FORC diagrams. Associating the FORC diagram with the Preisach diagram, we find that for moderate and weak interacting SD assemblages, the factorization interpretation of the Preisach diagram is correct, and in agreement with recent experimental results.