Housing Supply Expansion Act This bill modifies the federal prevailing wage rates that apply to the construction of federally assisted housing and requires the Department of Labor to convene a working group to review its process for determining prevailing wage rates. Specifically, the bill allows Labor to base the prevailing wage rates on rates in other geographic groupings (e.g., metropolitan statistical areas) besides civil subdivisions (e.g., counties) where the work is to be performed. The bill applies this modified methodology to public housing projects under various statutes. Additionally, the bill requires Labor to make no more than one wage rate determination for each project. The wage rate must be based on rates for residential construction (rather than rates for building construction or other categories). In addition, Labor must establish a working group of federal agencies and industry stakeholders to review and recommend revisions to prevailing wage rates for residential construction and affordable housing projects. The working group must recommend, for example, whether units with more than four floors should be classified as residential for purposes of prevailing wage rates.