  According to D.Zuo and an unpulished work of M.Bertola, there is a two--index
series of Dubrovin--Frobenius manifold structures associated to a B type
Coxeter group. We study the relations between these structures for the
different values of these indices. We show that part of the data of such
Dubrovin--Frobenius manifold indexed by $(k,l)$ can be recovered by the
$(k+r,l+r)$ Dubrovin--Frobenius manifold. Continuing the program of
arXiv:2007.11974 we associate an infinite system of commuting PDEs to these
Dubrovin--Frobenius manifolds and show that these PDEs extend the
dispersionless BKP hierarchy.
