Landscapes exhibiting multiple secondary structures arise in natural RNA molecules that modulate gene expression, protein synthesis, and viral infection [corrected]. We report herein that high-throughput chemical experiments can isolate an RNAs multiple alternative secondary structures as they are stabilized by systematic mutagenesis (mutate-and-map, M2) and that a computational algorithm, REEFFIT, enables unbiased reconstruction of these states structures and populations. In an in silico benchmark on non-coding RNAs with complex landscapes, M2-REEFFIT recovers 95% of RNA helices present with at least 25% population while maintaining a low false discovery rate (10%) and conservative error estimates. In experimental benchmarks, M2-REEFFIT recovers the structure landscapes of a 35-nt MedLoop hairpin, a 110-nt 16S rRNA four-way junction with an excited state, a 25-nt bistable hairpin, and a 112-nt three-state adenine riboswitch with its expression platform, molecules whose characterization previously required expert mutational analysis and specialized NMR or chemical mapping experiments. With this validation, M2-REEFFIT enabled tests of whether artificial RNA sequences might exhibit complex landscapes in the absence of explicit design. An artificial flavin mononucleotide riboswitch and a randomly generated RNA sequence are found to interconvert between three or more states, including structures for which there was no design, but that could be stabilized through mutations. These results highlight the likely pervasiveness of rich landscapes with multiple secondary structures in both natural and artificial RNAs and demonstrate an automated chemical/computational route for their empirical characterization.