Problem Definition: While physical (or 'social') distancing is an important public health intervention during airborne pandemics, physical distancing dramatically reduces the effective capacity of classrooms. During the COVID-19 pandemic, this presented a unique problem to campus planners who hoped to deliver a meaningful amount of in-person instruction in a way that respected physical distancing. This process involved 1) assigning a mode to each offered class as either remote, residential (in-person) or hybrid, and 2) reassigning classrooms under severely reduced capacities to the non-remote classes. These decisions need to be made quickly and under several constraints and competing priorities such as restrictions on changes to the timetable of classes, trade-offs between classroom density and educational benefits of in-person vs. online instruction, and administrative preferences for course modes and classrooms reassignments. Methodology and Results: We solve a flexible integer program and use hierarchical optimization to handle the multiple criteria according to priorities. We apply our methods using actual Georgia Tech (GT) student registration data, COVID-19 adjusted classroom and lab capacities, and departmental course mode delivery preferences. We generate optimal classroom assignments for all GT classes at the Atlanta campus, and quantify the trade-offs among the competing priorities. When classroom capacities decreased to 20 - 25% of their normal seating capacities, optimization afforded students 15.5% more in-person contact hours compared to no room re-assignments (NRR). Among sections with an in-person preference, our model satisfies 87% of mode preferences while only 47% are satisfied under NRR. Additionally, in a scenario in which all classes are preferred to be delivered in-person, our model can satisfy 90% of mode preferences compared to 37% under NRR. Managerial Implications: Multi-objective optimization is well-suited for classroom assignment problems that campus planners usually manage sequentially and manually. Our models are computationally efficient and flexible with the ability to handle multiple objectives with different priorities, build a new class-classrooms assignment or optimize an existing one, and can apply under normal or sudden capacity scarcity constraints.