This paper proposes a set of distributed real-time optimisation schemes for the steady-state optimisation of parametrically and structurally uncertain systems that are composed of multiple interconnected subsystems. These schemes are derived in the framework of modifier adaptation and use uncertain system models of varying complexity. Consequently, each distributed modifier-adaptation scheme imposes different requirements on the available plant measurements, the communication network, and the control architecture. We prove that every scheme can converge to the plant optimum despite model uncertainty and compare the main features of each approach. Finally, we illustrate our findings via a numerical example.