Mutation lower bound for Mandel oriented matroids

Determine whether there exist Mandel oriented matroids with fewer than three mutations adjacent to an element.

Background

Mandel oriented matroids are shown to be Las Vergnas and hence to have at least one adjacent mutation per element. The paper gives an upper bound of three for the minimum number in the considered setting and exhibits rank-four Mandel examples with an element having three adjacent mutations, but does not determine whether two or one can occur.