  We consider compact objects in a classical and non-relativistic
generalisation of Newtonian gravity, dubbed bootstrapped Newtonian theory,
which includes higher-order derivative interaction terms of the kind
generically present in the strong-field regime of gravity. By means of a field
redefinition, the original bootstrapped Newtonian action is written in a
canonical Newtonian form with non-linear source terms. Exact analytic solutions
remain unattainable, but we show that perturbative solutions of the canonical
theory can be efficiently used to derive approximate descriptions of compact
objects. In particular, using the canonical potential, we can more directly and
generally show that the Arnowitt-Deser-Misner mass differs from the (Newtonian)
proper mass due to the non-linear couplings in the theory. A few examples of
sources with different density profiles are explicitly reanalysed in this
framework.
