  We apply the BFFT formalism to a prototypical second-class system, aiming to
convert its constraints from second- to first-class. The proposed system admits
a consistent initial set of second-class constraints and an open potential
function providing room for applications to mechanical models as well as field
theory such as the non-linear sigma model. The constraints can be arbitralily
non-linear, broadly generalizing previously known cases. We obtain a sufficient
condition for which a simple closed expression for the Abelian converted
constraints and modified involutive Hamiltonian can be achieved. As explicit
examples, we discuss a particle on a torus and a spontaneous Lorentz symmetry
breaking vector model, obtaining in both situations the full first-class
abelianized constraints in closed form and the corresponding involutive
Hamiltonian.
