Stable isotope mixing models are used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets, plant nutrient use, geochemistry, pollution, and forensics. We describe an algorithm implemented as SISUS software for providing a user-specified number of probabilistic exact solutions derived quickly from the extended mixing model. Our method outperforms IsoSource [1], a deterministic algorithm for providing approximate solutions to represent the solution polytope. Our method is an approximate Bayesian large sample procedure. SISUS software is freely available at StatAcumen.com/sisus and as an R package at cran.r-project.org/web/packages/sisus.