Is a project multidisciplinary if only one unit is involved, but that unit, as interdisciplinary, might fall equally multiple eligible disciplines (e.g., humanities and social sciences)?

In the new Departmental Enhancement format, the Multi distinction is less important. Before there was a separate Multi competition with its own pot of money. Now there is one competition. Before the PI had to make a calculation as to whether the project would be more competitive in a multi competition or a stand-alone discipline-based competition. Now the distinction serves only as a guideline for the reviewers. Multi signifies a broad impact, and that the relationship of the departments needs to be examined by the panel, and that BoRSF needs to carefully consider which experts are assigned to review it. So it is important to understand, but will not affect which pot of money you are competing for.