Calcium-for-strontium cation substitution of the a(-)b(0)c(0)/b(0)a(-)c(0)-distorted, cation-ordered, n = 2 Ruddlesden-Popper phase, YSr2Mn2O7, leads to separation into two phases, which both retain an a(-)b(0)c(0)/b(0)a(-)c(0)-distorted framework and have the same stoichiometry but exhibit different degrees of Y/Sr/Ca cation order. Increasing the calcium concentration to form YSr0.5Ca1.5Mn2O7 leads to a change in the cooperative tilting on the MnO6 units to a novel a(-)b(-)c(-)/b(-)a(-)c(-) arrangement described in space group P2(1)/n11. Low-temperature, topochemical fluorination of YSr2Mn2O7 yields YSr2Mn2O5.5F3.5. In contrast to many other fluorinated n = 2 Ruddlesden-Popper oxide phases, YSr2Mn2O5.5F3.5 retains the a(-)b(0)c(0)/b(0)a(-)c(0) lattice distortion and P42/mnm space group symmetry of the parent oxide phase. The resilience of the a(-)b(0)c(0)/b(0)a(-)c(0)-distorted framework of YSr2Mn2O7 to resist symmetry-changing deformations upon both cation substitution and anion insertion/exchange is discussed on the basis the A-site cation order of the lattice and the large change in the ionic radius of manganese upon oxidation from Mn3+ to Mn4+. The structure property relations observed in the Y-Sr-Ca-Mn-O-F system provide insight into assisting in the synthesis of n = 2 Ruddlesden-Popper phases, which adopt cooperative structural distortions that break the inversion symmetry of the extended lattice and therefore act as a route for the preparation of ferroelectric and multiferroic materials.