Many online hate groups exist to disparage others based on race, gender identity, sex, or other characteristics. The accessibility of these communities allows users to join multiple types of hate groups (e.g., a racist community and a misogynistic community), raising the question of whether users who join additional types of hate communities could be further radicalized compared to users who stay in one type of hate group. However, little is known about the dynamics of joining multiple types of hate groups, nor the effect of these groups on peripatetic users. We develop a new method to classify hate subreddits and the identities they disparage, then apply it to understand better how users come to join different types of hate subreddits. The hate classification technique utilizes human-validated deep learning models to extract the protected identities attacked, if any, across 168 subreddits. We find distinct clusters of subreddits targeting various identities, such as racist subreddits, xenophobic subreddits, and transphobic subreddits. We show that when users become active in their first hate subreddit, they have a high likelihood of becoming active in additional hate subreddits of a different category. We also find that users who join additional hate subreddits, especially those of a different category develop a wider hate group lexicon. These results then lead us to train a deep learning model that, as we demonstrate, usefully predicts the hate categories in which users will become active based on post text replied to and written. The accuracy of this model may be partly driven by peripatetic users often using the language of hate subreddits they eventually join. Overall, these results highlight the unique risks associated with hate communities on a social media platform, as discussion of alternative targets of hate may lead users to target more protected identities.