Ahh. I can not really comprehend the consequence of that model. Estimates for my “real” data do seem practically unchanged, but estimates for the hypothetical data are a lot wider than if I fit the model with only “real” data and one hypothetical observation.
The best solution right now seems to be fitting a lot of very similar models. My model i rather small, and only takes about a minute to sample 4x2000 iters, so I may just let my CPU suffer and fit 200 very similar models.