  A formula for the structure constants of the multiplication of Schubert
classes is obtained in arXiv:1909.05283. In this note, we prove analogous
formulae for the Chern--Schwartz--MacPherson (CSM) classes and
Segre--Schwartz--MacPherson (SSM) classes of Schubert cells in the flag
variety. By the equivalence between the CSM classes and the stable basis
elements for the cotangent bundle of the flag variety, a formula for the
structure constants for the latter is also deduced.
