Real-world multiobjective optimization problems involve decision makers interested in a subset of solutions that meet their preferences. Decomposition-based multiobjective evolutionary algorithms (or MOEAs) have gained the research community’s attention because of their good performance in problems with many objectives. Some efforts have been made to propose variants of these methods that incorporate the decision maker’s preferences, directing the search toward regions of interest. Typically, such variants adapt the reference vectors according to the decision maker’s preferences. However, most of them can consider a single type of preference, the most common being reference points. Interactive MOEAs aim to let decision-makers provide preference information progressively, allowing them to learn about the trade-offs between objectives in each iteration. In such methods, decision makers can provide preferences in multiple ways, and it is desirable to allow them to select the type of preference for each iteration according to their knowledge. This article compares three interactive versions of NSGA-III utilizing multiple types of preferences. The first version incorporates a mechanism that adapts the reference vectors differently according to the type of preferences. The other two versions convert the preferences from the type selected by the decision maker to reference points, which are then utilized in two different reference vector adaptation techniques that have been used in a priori MOEAs. According to the results, we identify the advantages and drawbacks of the compared methods.