We argue for two crosslinguistic generalizations: T-V Optionality and *V-Aux. According to T-V Optionality, languages vary as to whether T is in a head-movement relation with a verb. *V-Aux states that in periphrasis, the lexical verb and the auxiliary cannot be related by head movement. Existing analyses of periphrasis can account for one or the other generalization, but not for both.
We further argue that this tension between the two generalizations is resolved if we adopt the hypothesis that both head movement and periphrasis are tied to selection. More specifically, we propose that head movement is parasitic on a selectional relation (following Svenonius 1994, Julien 2002, Matushansky 2006, and Preminger 2019) and that auxiliaries are merged as specifiers selected by functional heads such as T.