A growing number of empirical studies have quantified the degree to which evolution is geometrically parallel by estimating and interpreting pairwise angles between multiple replicate lineages' evolutionary change vectors in multivariate trait space. Similar comparisons, of distance in trait space, are used to assess the degree of convergence. These approaches amount to element-by-element interpretation of distance matrices, typically testing for differences among replicate evolutionary vectors, compared to a null hypothesis of perfect parallelism. We suggest a complimentary set of approaches, co-opted from evolutionary quantitative genetics, involving eigen analysis and comparison of among-lineage covariance matrices. Such approaches allow one to identify multiple major axes of evolutionary change (e.g., alternative adaptive solutions), and also allow for the definition of biologically tenable null hypotheses, such as drift, against which empirical patterns can be tested. Reanalysis of a dataset of multivariate evolution across a replicated lake/stream gradient in threespine stickleback reveals that most of the variation in the direction of evolutionary change can be captured in just a few dimensions, indicating a greater extent of parallelism than previously appreciated. We suggest that applying such multivariate approaches may often be necessary to fully understand the extent and form of parallel and convergent evolution.