Amgen Inc. has entered into two partnerships that the Thousand Oaks biotech hopes will eventually expand its product offerings to treat bowel disorders and colorectal cancer. Amgen will work with the Massachusetts General Hospital, the Broad Institute of Harvard and Massachusetts Institute of Technology to share research to develop treatments for inflammatory bowel disease, which now has a limited number of options. The Broad Institute receives major funding from a foundation founded by L.A. billionaire Eli Broad. The project will include collection and analysis of DNA samples from bowel disorder patients in an effort to identify genetic targets, probe gene function and develop drugs. Separately, San Diego drug developer Illumina Inc. said it signed an agreement with Amgen to develop a genetic diagnostic test for Amgen’s Vectibix, which treats late-stage colorectal cancer. Financial terms were not disclosed for either partnership, which were announced on Wednesday.