A subtle difference… or is it?
For your consideration:
“The provider took care of me” VS “The provider took care with me”
“She demonstrated feats of skill” VS “She demonstrated feats with skill”
“Tonight is the night of love” VS “Tonight is the night with love”
Using “of” tells us “why” we are doing something. Using “with” reminds us of “how” we should be doing it.