Stepping away from the more fantastic elements of Gumshoe to a straightforward procedural hunt for a serial killer, my immediate instinct is trying to set it in a local setting. Sadly, there aren't many local novels that stray into genre fiction. F. H. Batacan's Smaller and Smaller Circles is one of those rare books.
When F.H. Batacan first published Smaller and Smaller Circles—now acknowledged as the Philippines’ first crime novel—she was calling for a revolution. Or maybe two.
Early in Batacan’s prizewinning novel, the hero-sleuth, Jesuit priest and forensic anthropologist Father Gus Saenz, reveals his personal dream of overturning the popular national myth that there are no serial killers in the Philippines... F.H. Batacan also started a literary revolution by producing what is now widely acknowledged as the first Filipino crime novel. In the decade that has passed since its publication, others have begun to follow suit, and now the genre is burgeoning. (from the Soho Press blog)
The idea of having the a priest as the protagonist / detective in the Philippines is an interesting one, as it affords some latitude for the 'amateur sleuth' archetype in the predominantly Catholic country. They have a measure of respect that allows some access to otherwise prohibited locales of people, and their position in the political landscape of the Philippines affords them some protection from some of the ensconced powers-that-be.
Also, the nature of local crime scene investigation is exposed as being somewhat behind the more modern U.S. and U.K. approaches, rationalising why observation, deduction, psychology, and ground-pounding work are more than valid in a modern world where TV shows like C.S.I. became a phenomenon.
Perhaps more similar amateur detective archetypes can be thought up for a Philippine Gumshoe campaign.