The " zoom and filter " operations dear to the Shneiderman mantra are in reality not well specified in a data exploration context. There is a need to support users and suggest potential directions for exploration , and automatically selects a subset of nodes of interest based on a minimum initial user input. Filtering the data additionally avoids visual cluttering, especially overplotting, often resulting from laying out large networks. This paper explores how the multilayer properties of networks can be used to design a DOI (Degree of Interest) approach. Layers in a multilayer network bring nuances and must not be considered on an equal basis. We propose a method for extracting, expanding and displaying a sequence of sub-networks to guide users when exploring a multilayer network. Nodes and edges are selected based on an interest score computed for each node specifically taking the layer structure into account.