The paper presents a data-driven model of self-adaptivity for multiparty sessions. System choreography is prescribed by a global type. Participants are incarnated by processes associated with monitors, which control their behaviour. Each participant can access and modify a set of global data, which are able to trigger adaptations in the presence of critical changes of values. The use of the parallel composition for building global types, monitors and processes enables a significant degree of flexibility: an adaptation step can dynamically reconfigure a set of participants only, without altering the remaining participants, even if the two groups communicate.