  We analyze a recent conjecture regarding the perturbative construction of
non-linear deformations of all classically duality invariant theories,
including N=8 supergravity. Starting with an initial quartic deformation, we
engineer a procedure that generates a particular non-linear deformation
(Born-Infeld) of the Maxwell theory. This procedure requires the introduction
of an infinite number of modifications to a constraint which eliminates degrees
of freedom consistent with the duality and field content of the system. We
discuss the extension of this procedure to N=1 and N=2 supersymmetric theories,
and comment on its potential to either construct new supergravity theories with
non-linear Born-Infeld type duality, or to constrain the finiteness of N=8
supergravity.
