Fits Bayesian sparse conditional (Gaussian) mixture models for model-based clustering. Each mixture component factorizes into a chain of univariate polynomial regressions with per-component, per-equation Bayesian variable selection under a centered Zellner g-prior; the number of clusters is selected within a single run via an overfitted sparse mixture (Dirichlet concentration 1/K). The blocked Gibbs sampler draws the selection sets exactly by enumeration (or by validated single-flip Metropolis-Hastings in higher dimension), is provably well-posed under a documented proper fallback prior, and reports a label-invariant consensus partition (Dahl's least-squares criterion). Companion package to Dong, Liao, and Lee (2026), "Replacing three nested searches with one sweep: a Bayesian treatment of sparse conditional mixture clustering". Multiple-imputation functionality for the same engine is also exposed.