It does not matter what departments the participating faculty members work in when it comes to labeling the proposal Multi, or choosing a discipline to submit under. The participating departments check off the disciplines they represent. Hundreds of proposals have been submitted since I’ve been here with faculty working across departments on teams, and most of those probably were not Multi. Multi is department based. If more than one department from more than one discipline have vested roles in the project, then it is Multi. Creating the PI teams is a strategic element of the project but does not determine the disciplines the proposal is submitted under. If you are submitting under Humanities, it is a better bet to have a Humanities PI and not a Poli Sci PI, even if the Poli Sci PI did most of the writing. And if you are doing real Sociology work you probably want a Sociology person represented on the team to show the panel you have your bases covered. But none of that has to do with how the project is submitted. The department submits the proposal, the department chooses the discipline to submit under, and if they partner with another department they should look into the process for submitting and the process for formatting a Multi proposal and consider submitting as Multi.