Possibly is a 'modifier of uncertainty'* [a term I just made up.]
Like 'potentially', 'perhaps', 'might' or 'maybe' it's one of those words** someone uses when they think or estimate a situation has a ...
Some is an adverb there and Merriam-Webster has this (AE usage):
: in some degree : SOMEWHAT
felt some better
: to some degree or extent : a little
the cut bled some
I need to work on it some ...