A generic family of sixth-order modified Newton-like multiple-zero finders have been proposed in Geum et al. (2016). Among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight functions and study their dynamics by investigating the relevant parameter spaces and dynamical planes, via Mobius conjugacy map applied to a prototype polynomial of the form (z-a)(m) (z-b)(m). The resulting dynamics is best illustrated through a variety of parameter spaces as well as dynamical planes.