In this paper, we further develop the coordination control framework for discrete-event systems with both complete and partial observations. First, a weaker sufficient condition for the computation of the supremal conditionally controllable sublanguage and conditionally normal sublanguage is presented. Then we show that this condition can be imposed by synthesising a-posteriori supervisors. The paper further generalises the previous study by considering general, non-prefix-closed languages. Moreover, we prove that for prefix-closed languages the supremal conditionally controllable sublanguage and conditionally normal sublanguage can always be computed in the distributed way without any restrictive conditions we have used in the past.