1. A method, comprising: receiving, from an enterprise software application, a query with a data access service positioned between the enterprise software application and a plurality of multidimensional data sources, wherein the query conforms to a multidimensional query language specifying a set of multidimensional operations, and wherein the multidimensional data sources are supplied by different vendors and provide different implementations of the set of multidimensional operations; parsing the multidimensional query into a plurality of execution units with the data access service, wherein the execution units specify multidimensional operations required to perform the query; for each of the execution units: (i) determining, with the data access service, whether the implementation of the set of features of the target multidimensional data source supports any multidimensional operation specified by the execution unit, (ii) determining whether a local multidimensional calculation engine of the data access service is likely to perform the multidimensional operation more efficiently than a query processing engine of the target multidimensional data source, and (iii) designating the execution unit for either remote execution by a target one of the multidimensional data sources or locally by the data access service based on the determinations; and executing each of the multidimensional execution units locally with a multidimensional calculation engine within the data access service or remotely using a query processing engine of the target data source based on the designation.