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Abstract The gravitational microlensing method of discovering exoplanets and multi-star systems can produce degenerate solutions, some of which require in-depth analysis to uncover. We propose a new parameter space that can be used to sample potential solutions more efficiently and is more robust at finding all degenerate solutions for the “central-resonant” caustic degeneracy. We identified two new parameters,kandh, that can be sampled in place of the mass ratios and separations of the systems under analysis to identify degenerate solutions. The parameterkis related to the size of the central caustic, Δξ_c, whilehis related to the distance of a point along thekcontour from log(s) = 0, wheresis the projected planet-host separation. In this work, we present the characteristics of these parameters and the tests we conducted to prove their efficacy.