Multilingual research could offer a unique perspective on how the languages already acquired by a person affect the online processing of a new language. But it is currently difficult to assess this issue because theoretical accounts of multilingualism have focused on acquisition rather than processing and most empirical research to date has gathered untimed (offline) evidence. To help bridge this gap, we formulate hypotheses that can help derive processing predictions from existing accounts of multilingualism. But crucially, and based on previous findings in second language processing, we identify ways in which assumptions about crosslinguistic influence may need to be revised to allow the separate treatment of lexical and syntactic processing, and to consider the role of variables such as language dominance and proficiency. In our view, the question of what's special about multilingualism is worth studying, but more research is needed before we can begin answering it.