ValleyCare Health System, one of the last significant independents in the Bay Area, is seeking an affiliation with a larger partner, officials confirmed late Thursday. "We are exploring an affiliation with a number of potential partners," said spokeswoman Denise Bouillerce, adding that further details aren't immediately available. The nonprofit system, which boasts 242 beds and 300 on-staff physicians, serves a fairly well-to-do area in the outer East Bay, and could be an attractive merger candidate…