The algebra of M-nets, a high level class of labelled Petri nets, was introduced in the Petri Box Calculus in order to cope with the size problem of the low level nets, especially if applied as semantical domain for parallel programming languages. A general, unrestricted refinement operator intended to represent the procedure call mechanism for concurrent calls is introduced into the M-net calculus. Its coherence with the low level refinements is exhibited, together with its main properties.