Ordinal regression modeling of correlated sets of polytomous outcomes using the cumulative logits link function based on either individual outcomes or cumulative outcomes is addressed allowing for non-constant dispersions. For both of these two types of outcomes, formulations are provided for standard generalized estimating equations (GEE) modeling, for partially modified GEE modeling, for fully modified GEE modeling, and for extended linear mixed modeling (ELMM). These formulations include estimating equations, gradient vectors, and Hessian matrices. Alternate directly specified correlation structures and their estimation are also addressed.