I will not answer for Cyrillic, though the answer is yes.
I will cite from Nick Nicholas’ answer to Why is it possible for the Cyrillic script to be adopted in so many languages?
What made Greek script suited?
But it wasn’t repurposed that often, the languages it was repurposed for were usually not mainstream languages (or it was not the mainstream spelling of a mainstream language). And while there are traditions of both digraphs and diacritics in Greek, they have never become mainstream themselves: a little digraph work in Greek dialect (Cypriot, Tsakonian), diacritics limited to Greek dialectology. That means that it was not a very good fit for other languages most of the time.
So in theory: sure, just as Latin was suited: just add diacritics and digraphs. In practice: that would mean real work, and at best you’d have to kiss off legibility from Greeks as a design criterion:
Cf. the use of Greek to write Turkish: Nick Nicholas’ answer to How has it happened and Kemal Ataturk did not adopt Greek Alphabet, although in the Ottoman empire the Greek (and Cyrillic) were spoken?, and the Soviet Pontic use of digraphs: Pontic Greek