This paper explores how the operation of the interpretive complex (hit) is derived by phase heads (C, v, D), when the non-genitive possessor in the inalienable possession construction can undergo the peripheral movement (or A`-movement). The peripheral movement is only to induce structural configuration for focus, topic, operator, etc., at the edge of a phase, rather than to maintain feature-matching for Agree (Chomsky 2004). The analysis put forward in this paper is based on Chomsky`s (2004) recent claim that the peripheral movement is a non-Agree-driven movement, or a free internal merge to the edge of a phase due to the edge feature of the phase head (cf. Yang 2005). That is, edge effects are particularly motivated by an edge feature-driven movement. PIC forces movement to proceed successive-cyclically phase by phase. Three such pieces of evidence come from observations about the peripheral movement of the non-genitive possessor, Int effect and anaphor binding.