In 2013, Mukherje et al. developed the concept of interval-valued intuitionistic fuzzy soft multi set as a mathematical tool for making descriptions of the objective world more realistic, practical and accurate in some cases, making it very promising. In this paper we define some operations in interval-valued intuitionistic fuzzy soft multi set theory and show that the associative, distribution and De Morgan’s type of results hold in interval-valued intuitionistic fuzzy soft multi set theory for the newly defined operations in our way. Also, we define the necessity and possibility operations on interval-valued intuitionistic fuzzy soft multi set theory and study their basic properties and some results.