The Zilber-Pink conjecture is a central open problem in arithmetic geometry, which describes the interplay between local arithmetic behaviour and global geometric behaviour in terms of unlikely intersections. In joint work with Thomas Scanlon we proved a strong counterpart of Zilber-Pink describing the presence of likely intersections. We give an axiomatic set up where the proof works, which encompasses the many arithmetic varieties in which Zilber-Pink has been studied. In this talk I will describe the set up and our main theorem on likely intersections.