There is a growing need to introduce and develop computational models capable of faithfully modelling systems whose behaviour combines synchrony with asynchrony in a variety of complicated ways. Examples of such real-life systems can be found from VLSI hardware GALS systems to systems of cells within which biochemical reactions happen in synchronised pulses. One way of capturing the resulting intricate behaviours is to use Petri nets with localities where transitions are partitioned into disjoint groups within which execution is synchronous and maximally concurrent. In this paper, we generalise this type of nets by allowing each transition to belong to several localities. Moreover, we define this extension in a generic way for all classes of nets defined by net-types. We show that Petri nets with overlapping localities are an instance of the general model of nets with policies. Thanks to this fact, it is possible to automatically construct nets with localities from behavioural specifications given in terms of finite step transition systems. After that we outline our initial ideas concerning net synthesis when the association of transition to localities is not given and has to be determined by the synthesis algorithm.