Manufacturing USA Expansion Act of 2021 This bill expands the Manufacturing USA Program, which is a network of research institutes that collaborate to develop advanced manufacturing technologies. Specifically, the bill authorizes the National Institute of Standards and Technology, in coordination with other relevant federal agencies, to establish new institutes under the program and provide financial assistance awards and other supports for the program. The Department of Commerce must integrate into the program minority-serving institutions, historically Black colleges or universities, and tribal colleges or universities. Further, Commerce must establish policies to promote the domestic production of technologies developed through the program. Additionally, the bill establishes an advisory council for the program to make recommendations related to the manufacturing workforce.