  We discuss a scale-free model of bigravity, in which the mass parameter of
the standard bigravity potential is promoted to a dynamical scalar field. This
modification retains the ghost-free bigravity structure, in particular it
remains free of the Boulware-Deser ghost. We investigate the theory's
interaction structure, focusing on its consistent scaling limits and strong
coupling scales. Furthermore we explore the model's quadratic action, both
around generic background configurations and paying special attention to
cosmological backgrounds and to the associated background evolution. Finally we
consider the possibility of realizing a phase of late-time acceleration as well
as a quasi-de Sitter inflationary stage at early times, when the promoted "mass
scalar" becomes the inflaton.
