In order to access the influence of the RNH 3 cation on the symmetry of the perovskite cage network, we synthesized millimeter-sized single crystals of the n = 2 and n = 3 variants of (RNH 3 ) 2 (MA) n-1 Pb n I 3n+1 with RNH 3 being one of BA, PEA, TPMA and MA being methylammonium. Figure shows the crystal structures of our samples. Note that we have established the exact single-crystal structure of (PEA) 2 (MA)Pb 2 I 7 based on the data collected from a high quality crystal at 100 K. The synthesis details, optical micrographs (Figure ), and powder X-ray diffraction patterns (Figure ) confirming the phase purity of these compounds are all presented in the SI. In our measurements we use a backscattering (also known as reflective or epi ) geometry to collect SHG and THG in order to minimize absorption and phase-mismatch effects. As discussed in the SI, the sampling depth SHG and THG is constrained by phase-matching to be less than 100 nm. To perform the multidimensional harmonic generation measurements, we use an ultrafast optical parametric amplifier (OPA) to generate tunable near-IR light. This light passes through a variable neutral density filter and is loosely focused onto the sample. The SHG and THG are selected by an aperture, spectrally resolved with a monochromator, and detected with a photomultiplier tube. To intentionally measure PL and mPL, we remove the aperture and excite with 3.1 eV (400 nm) or 0.99 eV (1250 nm) light, respectively; note that the collection efficiency of our photoluminescence apparatus is very low compared to a traditional PL microscope because our long focal length collection mirror leads to a numerical aperture of merely ∼ 0.05. Additional details about our multidimensional spectrometer are described in the SI. Note that our methodology is similar to the shifted excitation difference technique used in the resonance and stimulated Raman community to remove fluorescence interference. Our main spectroscopic results are shown in Figure , in which we measure the output intensity for six different samples as a function of both excitation OPA frequency, ω, and emission frequency, ω m . The most consistent and prominent feature in all six spectra (right hand side) has an excitation/emission frequency dependence of ω m = 3 ω. This feature is THG. The 2D-RP perovskites with PEA and TPMA spacer cations show a weaker but definitive feature which goes as ω m = 2 ω. Note that this feature is SHG. Conversely, no SHG is observed for 2D-RP perovskites with BA spacer cations. Here, conclusive assignments of SHG and THG are not based merely on the presence or absence of an emission feature, but rather the scaling relationship of the emission features.