The orbit of Dysnomia around Eris has been investigated since its discovery in 2005. Attempts to fit current observations of Dysnomia with a Keplerian orbit have failed to produce good answers, where the best Keplerian model fails to match the data at the 6.3-sigma level. This failure does not appear to be associated with systematic errors. To apply a Non-Keplerian analysis, we have previously developed and validated an n-quadrupole integrator SPINNY (SPIN + N-bodY) which can include all the dominant non-Keplerian effects relevant within observational precision. SPINNY has been combined with advanced Bayesian model fitting for KBO astrometry in our modeling tool called MultiMoon. Using MultiMoon, we explore the shapes of Eris and Dysnomia, searching for values of oblateness and prolateness in both objects that would fit the non-synchronous orbit of Dysnomia. We also explore the possibility of a second satellite orbiting Eris with a tight inner orbit, and present the likelihoods and data of both analyses.