Uniaxial negative thermal expansion (NTE) is known to occur in low $n$ members of the An+1$BnO3n+1 Ruddlesden–Popper layered perovskite series with a frozen rotation of BO_6 octahedra about the layering axis. Previous work has shown that this NTE arises due to the combined effects of a close proximity to a transition to a competing phase, so called “symmetry trapping”, and highly anisotropic elastic compliance specific to the symmetry of the NTE phase. We extend this analysis to the broader Ruddlesden-Popper family (n = 1, 2, 3, 4,..), demonstrating that by changing the fraction of layer interface in the structure (i.e. the value of 1/n) one may control the anisotropic compliance that is necessary for the pronounced uniaxial NTE observed in these systems. More detailed analysis of how the components of the compliance matrix develop with 1/n allows us to identify different regimes, linking enhancements in compliance between these regimes to the crystallographic degrees of freedom in the structure. We further discuss how the perovskite layer thickness affects the frequencies of soft zone boundary modes with large negative Gruneisen parameters, associated with the aforementioned phase transition, that constitute the thermodynamic driving force for NTE. This new insight complements our previous work — showing that chemical control may be used to switch from positive to negative thermal expansion in these systems — since it makes the layer thickness, n, an additional well-understood design parameter that may be used to engineer layered perovskites with tuneable thermal expansion. In these respects, we predict that, with appropriate chemical substitution, the n = 1 phase will be the system in which the most pronounced NTE could be achieved.