Mixed cation perovskites, [HC(NH2)2]xCs(1-x)PbI3, (FAxCs(1-x)PbI3) with x=0.8 achieve high solar cell power conversion efficiencies (PCEs) while exhibiting long-term stability under ambient conditions. In this work, we perform density functional theory (DFT) calculations, first-principles molecular dynamics (MD) simulations, solid-state nuclear magnetic resonance (NMR) and X-ray powder diffraction (XRD) measurements aimed at investigating the possible phase stability of Cs+-rich FAxCs(1-x)PbI3, (0≤x≤0.5) mixed-cation materials as potential candidates for tandem solar cell applications. Estimations of the free energy of the mixtures with respect to the pure compounds together with calculations of the relative phase stability at 0 K and at finite temperature show that although the mixtures can form, the δ phase remains the thermodynamically most stable phase at room temperature. This is fully corroborated by solid-state NMR and XRD measurements and is in contrast to FA+-rich Cs/FA mixtures where small additions of Cs+ are sufficient to stabilize the perovskite phase at ambient conditions. The atomistic origin for this contrasting behavior arises from an energetic destabilization of the perovskite phase on the one hand caused by the incorporation of a large cation (FA+) into the relatively small host lattice of γ-CsPbI3 and on the other hand is induced by the lower degree of distortion of the host lattice. These observations allow us to propose a new design principle for the preferential stabilization of the perovskite phase over the competing δ phase.