We study a continuous-time principal--multi-agent problem in which the principal has standard expected-utility preferences, while the agents evaluate their terminal compensations through criteria that depend non-linearly on conditional expectations of both the state process describing the common project and their own terminal compensations, with mean-variance preferences as a canonical example. The agents are therefore time-inconsistent and are modelled as sophisticated decision makers who anticipate the future revisions of their successive selves. Since their actions jointly affect the evolution of the common project, their response to a contract must constitute an equilibrium both across agents and over time, which we refer to as a sub–game-perfect Nash equilibrium. Building on the BSDE characterisation of such equilibria in time-inconsistent stochastic differential games, we show that the principal’s problem can be reformulated as a stochastic control problem subject to stochastic target constraints encoding the relevant terminal compatibility conditions. In the Markovian setting, we characterise the principal’s value function through a system of Hamilton–Jacobi–Bellman equations in the viscosity sense.