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Recently, a computational algorithm based on Bayesian data analysis was presented to invert the linear rheology of branched polymers [Shanbhag, S., Rheol. Acta 49, 411-422 (2010)]. When rheological data of an unknown polymer mixture are supplied, the algorithm produces an exhaustive distribution of structures and compositions, consistent with the rheology. Frequently, it identifies multiple or degenerate structures. In this proof-of-concept paper, a resolution of the degeneracy is sought by appealing to the concept of combinatorial rheology [Larson, R. G., Macromolecules 34, 4556-4571 (2001)], where the unknown sample is strategically blended with a well-characterized fraction. Experimental load is alleviated by identifying the optimal type, molecular weight, and composition of the polymer fraction to blend with the unknown sample, to discriminate between the degenerate structures, most conclusively. Two methods are proposed and tested on a particular mixture that is characterized by severe degeneracy. Both proposed methods are able to correctly identify the structure and composition of the original mixture by requiring two additional rheological experiments. [ABSTRACT FROM AUTHOR]