Mission Impossible (3 and 4) and Star Trek showed that Giacchino can do wonders with existing themes - Star Trek in particular managed to be both a great Trek score and a great Giacchino score, no mean feat.
Not to mention the incredible stuff he did for Lost - the evolution of character themes in that were at times quite stunning (unlike Williams' underwhelming efforts with the Anakin/Vader themes, and I don't think that can be entirely attributed to bad editing).