A conversational recommender system (CRS) is a practical application for item recommendation through natural language conversation. Such a system estimates user interests for appropriate personalized recommendations. Users sometimes have various interests in different categories or genres, but existing studies assume a unique user interest that can be covered by closely related items. In this work, we propose to model such multiple user interests in CRS. We investigated its effects in experiments using the ReDial dataset and found that the proposed method can recommend a wider variety of items than that of the baseline CR-Walker.