This paper describes a strategy for a general search used by the ATLAS Collaboration to find potential indications of new physics. Events are classified according to their final state into many event classes. For each event class an automated search algorithm tests whether the data are compatible with the Monte Carlo simulated expectation in several distributions sensitive to the effects of new physics. The significance of a deviation is quantified using pseudo-experiments. A data selection with a significant deviation defines a signal region for a dedicated follow-up analysis with an improved background expectation. The analysis of the data-derived signal regions on a new dataset allows a statistical interpretation without the large look-elsewhere effect. The sensitivity of the approach is discussed using Standard Model processes and benchmark signals of new physics. As an example, results are shown for 3.2fb-1 of proton-proton collision data at a centre-of-mass energy of 13TeV collected with the ATLAS detector at the LHC in 2015, in which more than 700 event classes and more than 105 regions have been analysed. No significant deviations are found and consequently no data-derived signal regions for a follow-up analysis have been defined.