Statistical tests for assessing marginal homogeneity of matched-pair polytomous data can be classified as a score-type test or a Wald-type test; the Wald-type Bhapkar test is a more powerful alternative to the score-type Stuart–Maxwell test, and the Bhapkar test tends to be liberal. Extending the authors’ earlier work, an additional test of each classification is proposed for testing marginal homogeneity, and the relationships among the available test statistics are established. The results from some limited simulation study suggest that the new proposals are very competitive alternatives to the extant methods. These results are the basis of the authors’ recommendations to practitioners. Information from SAS procedure PROC CATMOD regarding Bhapkar’s test statistic and the relationship among the test statistics make their implementation and calculation convenient and accessible to interested researchers.