We describe a simple prescription by which distinct (non-equilibrium) steady states, namely fixed points of dynamical semi-groups, can be classified in terms of eigenvalues of a globally conserved quantity, i.e. a unitary operator which simultaneously commutes with the Hamiltonian and the set of all Lindblad (jump) operators. As an example, we study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global `microcanonical' constraint, i.e. conserving the total magnetization. Interestingly, numerical simulations suggest that a pair of distinct non-equilibrium steady states becomes indistinguishable in the thermodynamic limit, and exhibit sub-diffusive spin transport in the easy-axis regime.