multiggm_mcmc(method = "mghs") fits the multiple graphical horseshoe (Busatto & Stingo 2025), adapted from github.com/cbusatto/mGHS. It returns a multiggm_fit, so coef(), fitted(), posterior_pcor(), posterior_ci(), diff_prob_pcor(), plot_trace("theta") and multi-chain fitting work. It reproduces upstream’s draws exactly for the same seed (inst/mghs/VALIDATION.md). Local fixes: rejection samplers that could hang, stuck checks that missed NaN, and a cut-model indexing bug (inst/mghs/UPSTREAM.md). New options: thin, save_draws = FALSE (keep only running summaries), automatic restart of stuck chains.