We introduce three-color alternating-laser excitation (3c-ALEX), a fluorescence resonance energy transfer (FRET) method that measures up to three intramolecular distances and complex interaction stoichiometries of single molecules in solution. This tool extends substantially the capabilities of two-color ALEX, which employs two alternating lasers to study molecular interactions (through probe stoichiometry S) and intramolecular distances (through FRET efficiency E), and sorts fluorescent molecules in multi-dimensional probe-stoichiometry and FRET-efficiency histograms. Probe-stoichiometry histograms allowed analytical sorting, identification, and selection of diffusing species; selected molecules were subsequently represented in FRET-efficiency histograms, generating up to three intramolecular distances. Using triply labeled DNAs, we established that 3c-ALEX enables 1), FRET-independent analysis of three-component interactions; 2), observation and sorting of singly, doubly, and triply labeled molecules simultaneously present in solution; 3), measurements of three intramolecular distances within single molecules from a single measurement; and 4), dissection of conformational heterogeneity with improved resolution compared to conventional single-molecule FRET. We also used 3c-ALEX to study large biomolecules such as RNA polymerase-DNA transcription complexes, and monitor the downstream translocation of RNA polymerase on DNA from two perspectives within the complex. This study paves the way for advanced single-molecule analysis of complex mixtures and biomolecular machinery.