Holders of life insurance policies can exercise various options that lead to contract modifications, e.g. full surrender, partial surrender, paid-up and dynamic premium increase options. Transitions between these contract states materially affect (current and future) cash flows, and thus represent a serious source of uncertainty for an insurance company. It is common practice to model these transitions independently, i.e. without considering joint determinants of the different aspects of policyholder behaviour. Our paper shows how consistent best estimate transition rates for multiple status transitions can be derived using data science methods. More specifically, we extend existing multivariate approaches with the Lasso method such that the key drivers for each transition can be identified automatically. We discuss the performance, the complexity and the practical applicability of the different modelling approaches based on data from a European insurer.