The Glashow-Iliopoulos-Maiani mechanism is extremely efficient to suppress the flavour-changing neutral current decays of charmed hadrons induced by the c → u transitions, making such processes particularly sensitive to phenomena beyond the Standard Model. In particular, c → u decays with a neutrino pair in the final state are theoretically appealing due to the small long-distance contributions. Moreover, in the framework of the Standard Model Effective Field Theory (SMEFT), the SU (2) L invariance allows to relate the Wilson coefficients in the effective Hamiltonian governing the c → uν ν decays to the coefficients in the c → u + − Hamiltonian. We analyze the B c → B ( * )+ ν ν decays, for which branching fractions of at most O(10 −16 ) are predicted in the Standard Model including short-and long-distance contributions, so small that they can be considered as null tests. Using SMEFT and the relation to the c → u + − processes we study the largest enhancement achievable in generic new physics scenarios. Then we focus on a particular extension of the Standard Model, the 331 model. SMEFT relations and the connection with c → u + − imply that B(B c → B ( * )+ ν ν) could even reach O(10 −6 ), an extremely large enhancement. A less pronounced effect is found in the 331 model, with O(10 −11 ) predicted branching fractions. Within the 331 model correlations exist among the B c → B ( * )+ ν ν and K → πν ν, B → (X s , K, K * )ν ν channels.