  We show that quantum Casimir W-algebras truncate at degenerate values of the
central charge c to a smaller algebra if the rank is high enough: Choosing a
suitable parametrization of the central charge in terms of the rank of the
underlying simple Lie algebra, the field content does not change with the rank
of the Casimir algebra any more. This leads to identifications between the
Casimir algebras themselves but also gives rise to new, `unifying' W-algebras.
For example, the kth unitary minimal model of WA_n has a unifying W-algebra of
type W(2,3,...,k^2 + 3 k + 1). These unifying W-algebras are non-freely
generated on the quantum level and belong to a recently discovered class of
W-algebras with infinitely, non-freely generated classical counterparts. Some
of the identifications are indicated by level-rank-duality leading to a coset
realization of these unifying W-algebras. Other unifying W-algebras are new,
including e.g. algebras of type WD_{-n}. We point out that all unifying quantum
W-algebras are finitely, but non-freely generated.
