In typical differential item functioning (DIF) assessments, an item's DIF status is not influenced by its status in previous test administrations. An item that has shown DIF at multiple administrations may be treated the same way as an item that has shown DIF in only the most recent administration. Therefore, much useful information about the item's functioning is ignored. In earlier work, we developed the Bayesian updating (BU) DIF procedure for dichotomous items and showed how it could be used to formally aggregate DIF results over administrations. More recently, we extended the BU method to the case of polytomously scored items. We conducted an extensive simulation study that included four "administrations" of a test. For the single-administration case, we compared the Bayesian approach to an existing polytomous-DIF procedure. For the multiple-administration case, we compared BU to two non-Bayesian methods of aggregating the polytomous-DIF results over administrations. We concluded that both the BU approach and a simple non-Bayesian method show promise as methods of aggregating polytomous DIF results over administrations.