Membrane reshaping proteins are important for a number of physiological cellular processes such as vesicle and viral budding, cell division and membrane repair. Recently, a new mechanism for reshaping membranes has been proposed via the study of ESCRT-III filaments. This mechanism involves the sequential exchange of filament composition to increase filament curvature which drives the deformation and scission of membranes. However, the relationship between the filament composition and its mechanical effect is lacking. We develop a kinetic model for the assembly of composite filaments that includes protein–membrane adhesion, filament mechanics and membrane mechanics. We identify the physical conditions for such a membrane remodelling and show this mechanism is efficient because sequential polymer assembly lowers the energetic barrier or membrane deformation. Beyond their biological application, our findings lay the groundwork for designing shape-shifting materials at the nanoscale.