Traditionally, a preference on a set A of alternatives is modeled by a binary relation R on A satisfying suitable axioms of pseudo-transitivity, such as the Ferrers condition (aRb and cRd imply aRd or cRb) or the semitransitivity property (aRb and bRc imply aRd or dRc). In this paper we study (m,n)-Ferrers properties, which naturally generalize these axioms by requiring that a1R…Ram and b1R…Rbn imply a1Rbn or b1Ram. We identify two versions of (m,n)-Ferrers properties: weak, related to a reflexive relation, and strict, related to its asymmetric part. We determine the relationship between these two versions of (m,n)-Ferrers properties, which coincide whenever m+n=4 (i.e., for the classical Ferrers condition and for semitransitivity), otherwise displaying an almost dual behavior. In fact, as m and n increase, weak (m,n)-Ferrers properties become stronger and stronger, whereas strict (m,n)-Ferrers properties become somehow weaker and weaker (despite failing to display a monotonic behavior). We give a detailed description of the finite poset of weak (m,n)-Ferrers properties, ordered by the relation of implication. This poset depicts a discrete evolution of the transitivity of a preference, starting from its absence and ending with its full satisfaction.