  A class of quantum chains possessing a family of local conserved charges with
a Catalan tree pattern is studied. Recently, we have identified such a
structure in the integrable $SU(N)$-invariant chains. In the present work we
find sufficient conditions for the existence of a family of charges with this
structure in terms of the underlying algebra. Two additional systems with a
Catalan tree structure of conserved charges are found. One is the spin 1/2 XXZ
model with $\Delta=-1$. The other is a new octonionic isotropic chain,
generalizing the Heisenberg model. This system provides an interesting example
of an infinite family of noncommuting local conserved quantities.
