To be capable of working with people of different cultures on a project without having any conflicts is the ability we must possess.
"Of different cultures" is an adjective describing "people"
and I think "with people of different cultures" "on a project" "without having any conflicts" should be adverbs that modify "working" instead of adjective phrases that modify the noun in front of it?
"on a project" is not an adjective for "cultures"
"without having any conflicts" is not an adjective for" project"
Am I right about this?
If what I wrote is correct, then it seems like multiple adverbial prepositional phrases are used to modify the same verb , is this acceptable?