The distribution of phase-unlocking and phase-edge movement and its implications for phase theory

My proposal has two goals: (i) to establish the distributions of two different strategies for extracting from phases - edge-movement and unlocking; and (ii) to amend phase theory so that it derives this. Goal-(i) matters because, contra most prior assumptions, recent work suggests both edge-movement/unlocking occur, in complementary distribution: some
types of movement out of phases involve passing through the phase-edge; other types don't, but the phase-head must
be Agreed with qua 'unlocked'. This applies to DP (Branan & Davis 2019, B&D; Branan 2018, B), and also CP given
evidence for edge-movement through spec-CP (e.g. van Urk 2019) but also unlocking (Rackowski & Richards 2005, Van
Urk & Richards 2015). I plan to use cross-linguistic evidence to work out what determines the distribution. Prior
suggestions include a contrast between unlocking for deeply-embedded material (B&D) or for material for which edge-movement is anti-local (B), edge-movement elsewhere - but this involves DP only, and isn't applied cross-linguistically.
Crucially, this also requires amending phase theory. Standard phase-theory only allows edge-movement, because
phases Transfer material out of syntax once completed - so it can't be rescued by subsequent 'unlocking'. I'd pursue an
intervention-based 'phase' theory, expanding recent work reducing phasehood (Thivierge 2021) and edge-movement
(Keine & Zeijlstra 2021) to (phi-)intervention. This would allow reducing locality to one notion, intervention.