To shed light on findings suggesting that not all job crafting strategies are (equally) favourable for employee motivation, we applied cusp catastrophe models to explore the possibility that combinations of job crafting strategies might be associated with nonlinear changes in work engagement (i.e., vigour, dedication, and absorption). We used cross-sectional data from a heterogeneous sample of 193 Greek employees and investigated increasing social and structural job resources as asymmetry factors, and increasingly challenging job demands and decreasingly hindering job demands as bifurcation factors in relation to work engagement. Cusp models, analysed with the maximum likelihood and least squares methods, proved superior to their linear alter-natives. Increasing social job resources functioned as the asymmetry factor for vigour and dedication. Increasing structural job resources was the asymmetry factor for absorption. The bifurcation factors were decreasing hindering job demands for vigour and increasing job challenges for dedication and absorption. This evidence suggests that threshold values exist in decreasing hindering and increasing challenging job demands, beyond which sudden changes in work engagement occur. The supported nonlinear models add in explaining when job crafting strategies are unfavourable for employees and have epistemological implications by suggesting that the underlying processes may be viewed as a complex dynamical system.