Investigations of statistical power in causal mediation analysis are scant, especially for binary outcomes. In parallel, categorical mediators are not rare in epidemiologic practice. In the present work, we aim to generalize our exact regression-based approach for a binary outcome and a binary mediator to mediation settings with a categorical mediator. Namely, we will introduce exact natural effect estimators based on binary outcome and multinomial mediator logistic models. Formulas for the delta method standard errors will be also provided. Since the flexibility of a mediation analysis with a categorical mediator comes at a cost in terms of power, we will present results of a simulation study designed to evaluate capacity to detect natural indirect effect under different scenarios, including ones where the outcome is affected by certain categories of the mediator but not necessarily by others.