The subjects of multifunctions and parameterised optimisation are as important as ever. Consumer behaviour (Big Data), cosmology and astronomy (thanks to the enormous amount of high precision data), health, weather, society... In many cases non-static data can be a subject for multifunction analysis, and many non-static real-life problems can be transformed into parameterised optimisation problems. In this publication, a new concept of multifunction differentiation is proposed, relevant basic calculus is built, and is applied to parameterised optimisation problems with parameterised constraints. A generic approach to solving such problems is proposed.