In this paper our main task is to show the existence of one point pairwise QHC extensions of a non pairwise QHC space. Two such extensions are constructed which are shown to be respectively projectively maximum and minimum in the class of all such one point pairwise QHC extensions. For this purpose the notion of locally pairwise QHC spaces are introduced. It is shown, in addition, that the classical set-topological characterization of a locally QHC space in terms of the remainders of arbitrary QHC extensions fails here. Nevertheless, it has been possible to establish one side of the characterization for any bitopological space.