M-logic can be modified in various directions. We can weaken M-logic although its strengthening is certainly more interesting. Generally, ways of these modification are similar to those of the classical logic. Thus we will present a free version of M-logic and its several extension to modal logic. Also we will show how M-logic, as the generalised quantifier extension of classical logic, can be applied to generalise the traditional possible world semantics to the so-called non-standard possible world semantics and, consequently, to generalise the traditional propositional modal logic. We are not going to present in each case fully developed syntactic and semantic systems and prove all their fundamental metalogical properties. Rather we focus on their philosophically relevant formal features (and omit those which, we hope, can be easily completed by the reader, or which are extremely technical, as in the case of modal M-logic). Semantical considerations will be given priority here since they are formally more convenient and easier for ontological interpretations than syntactic ones.