The dome of Santa Maria del Fiore, Florence Cathedral, was built between 1420 and 1436 by architect Filippo Brunelleschi and it is now cracking under its own weight. Engineering efforts are under way to model the dome’s structure and reinforce it against further deterioration. According to some scholars, Brunelleschi might have built reinforcement structures into the dome itself; however, the only known reinforcement is a wood chain 7.75 m above the springing of the Cupola. Multiple scattering muon radiography is a non-destructive imaging method that can be used to image the interior of the dome’s wall and therefore ascertain the layout and status of any iron substructure in it. A demonstration measurementwas performed at the Los Alamos National Laboratory on a mock-up wall to show the feasibility of the work proposed, and a lightweight and modular imaging system is currently under construction. We will discuss here the results of the demonstration measurement and the potential of the proposed technique, describe the imaging system under construction and outline the plans for the measurement. This article is part of the Theo Murphy meeting issue ‘Cosmic-ray muography’.