This paper focuses on prosodic adjunction at the Prosodic Word level in a polysynthetic language. I argue that recursion at a depth of more than two levels can only be generated by a theory which requires exact correspondence between certain syntactic phrases and Prosodic Words. Such a theory is similar to Phonological Phrase correspondence in Match Theory, suggesting there is an underlying shared property between correspondence at the Prosodic Word and Phonological Phrase levels. In addition, this theory must include a constraint which prohibits recursive prosodic constituents in order to generate the attested typology of clitics across languages. The empirical focus is the prosodic structure of the verbal complex in Blackfoot (Algonquian; ISO 639-3: bla). Using phonotactic evidence I argue that the vP phase corresponds to a Prosodic Word, and that each prefix to the stem is a Prosodic Word adjunct. I then compare several theories of the syntax-prosody interface, including versions of Alignment Theory, Wrap Theory, and Match Theory. A subset of schematic candidates with one or two prefixes to a stem are used to determine which theories generate the attested typology of clitics as well as a multiply recursive Prosodic Word structure.