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Multiverse analyses involve conducting all combinations of reasonable choices in a data analysis process. A reader of a study containing a multiverse analysis might question—are all the choices included in the multiverse reasonable and equally justifiable? How much do results vary if we make different choices in the analysis process? In this work, we identify principles for validating the composition of, and interpreting the uncertainty in, the results of a multiverse analysis. We present Milliways, a novel interactive visualisation system to support principled evaluation of multiverse analyses. Milliways provides interlinked panels presenting result distributions, individual analysis composition, multiverse code specification, and data summaries. Milliways supports interactions to sort, filter and aggregate results based on the analysis specification to identify decisions in the analysis process to which the results are sensitive. To represent the two qualitatively different types of uncertainty that arise in multiverse analyses—probabilistic uncertainty from estimating unknown quantities of interest such as regression coefficients, and possibilistic uncertainty from choices in the data analysis—Milliways uses consonance curves and probability boxes. Through an evaluative study with five users familiar with multiverse analysis, we demonstrate how Milliways can support multiverse analysis tasks, including a principled assessment of the results of a multiverse analysis.