MULTIGRIS (also called mgris) uses the sequential Monte Carlo method in PyMC (ascl:1506.005) to extract the posterior distributions of primary grid parameters and predict unobserved parameters/observables. The code accepts either a discrete number of components and/or continuous (e.g., power-law, normal) distributions for any given parameter. MULTIGRIS, written in Python, infers the posterior probability functions of parameters in a multidimensional potentially incomplete grid with some observational tracers defined for each parameter set. Observed values and their potentially asymmetric uncertainties are used to calculate a likelihood which, together with predefined or custom priors, produces the posterior distributions. Linear combinations of parameter sets may be used with inferred mixing weights and nearest neighbor or linear interpolation may be used to sample the parameter space.