Very high risk neuroblastoma is characterised by increased MAPK signalling, and targeting MAPK signalling is a promising therapeutic strategy. We used a deeply characterised panel of neuroblastoma cell lines and found that the sensitivity to MEK inhibitors varied drastically between these cell lines. By generating quantitative perturbation data and mathematical modelling, we determined potential resistance mechanisms. We found that negative feedbacks within MAPK signalling and via the IGF receptor mediate re-activation of MAPK signalling upon treatment in resistant cell lines. By using cell-line specific models, we predict that combinations of MEK inhibitors with RAF or IGFR inhibitors can overcome resistance, and tested these predictions experimentally. In addition, phospho-proteomic profiling confirmed the cell-specific feedback effects and synergy of MEK and IGFR targeted treatment. Our study shows that a quantitative understanding of signalling and feedback mechanisms facilitated by models can help to develop and optimise therapeutic strategies. Our findings should be considered for the planning of future clinical trials introducing MEKi in the treatment of neuroblastoma.