Full Idea
We should think of possibility as potentiality in abstraction from its bearer. So 'it is possible that p' is defined as 'something has an iterated potentiality for it to be the case that p'.
Clarification
'Iterated' implies there could be chains of potentialities
Gist of Idea
Possibility is a generalised abstraction from the potentiality of its bearer
Source
Barbara Vetter (Potentiality [2015], 1.4)
Book Reference
Vetter,Barbara: 'Potentiality: from Dispositions to Modality' [OUP 2015], p.18
A Reaction
If possibilities are abstractions from potentialities, I am inclined the treat potentialities as abstractions from dispositions, and dispositions (and properties) as abstractions from powers. Powers are not abstractions - they are the reality.