IN THE BEGINNING, it’s a kind of ravenous search for inspiration,” says Brad Cloepfil of the projects taken on by Allied Works, the architectural practice he founded in 1994. He starts each assignment not with 3-D models and renderings, but with a series of abstract charcoal-and-pastel drawings and sculptural studies. They’re two elements of an unorthodox approach that has allowed his relatively small firm (fewer than 40 people between the Portland, Oregon, and New York City offices) to compete with much bigger names. He lost out to David Chipperfield, for instance, on the expansion of New York’s Metropolitan Museum...