The stability and formation of a perovskite structure is dictated by the Goldschmidt tolerance factor as a general geometric guideline. The tolerance factor has limited the choice of cations (A) in 3D lead iodide perovskites (APbI3), an intriguing class of semiconductors for high-performance photovoltaics and optoelectronics. Here, we show the tolerance factor requirement is relaxed in 2D Ruddlesden-Popper (RP) perovskites, enabling the incorporation of a variety of larger cations beyond the methylammonium (MA), formamidinium, and cesium ions in the lead iodide perovskite cages for the first time. This is unequivocally confirmed with the single-crystal X-ray structure of newly synthesized guanidinium (GA)-based (n-C6H13NH3)2(GA)Pb2I7, which exhibits significantly enlarged and distorted perovskite cage containing sterically constrained GA cation. Structural comparison with (n-C6H13NH3)2(MA)Pb2I7 reveals that the structural stabilization originates from the mitigation of strain accumulation and self-adjustable strain-balancing in 2D RP structures. Furthermore, spectroscopic studies show a large A cation significantly influences carrier dynamics and exciton-phonon interactions through modulating the inorganic sublattice. These results enrich the diverse families of perovskite materials, provide new insights into the mechanistic role of A-site cations on their physical properties, and have implications to solar device studies using engineered perovskite thin films incorporating such large organic cations.