I asked something similar here a while back. One /could/ write a function that calls stan for X iterations, tests convergence, if not at threshold, then call stan again and append the samples to the previous samples.
Ideally, one could literally pick up one where left off using the final posterior sample of the first X iterations as the inits for the second (and so on), but iirc the stan devs said they don't have a way of specifying or returning (can't recall which) the mass matrix and other warmup parameters so that one could skip warmup and jump straight to where you left off.