Pseudo-ASL structure with bipermanents

Determine whether the coordinate ring of n×m matrices admits a pseudo-ASL structure whose standard monomials are standard bipermanents and for which a pseudo-ASL term order exists.

Background

While straightening laws for bipermanents are known, it is unclear whether they furnish a full pseudo-ASL structure with an admissible term order replacing the bideterminant setting. A positive resolution would enable a Gröbner-like theory for permanental ideals analogous to the determinantal case.