The distributions output by a standard (non-normalized) conformal predictive system all have the same shape but differ in location, while a normalized conformal predictive system outputs distributions that differ also in shape, through rescaling. An approach to further increasing the flexibility of the framework is proposed, called Mondrian conformal predictive distributions, which are (standard or normalized) conformal predictive distributions formed from multiple Mondrian categories. The effectiveness of the approach is demonstrated with an application to regression forests. By forming categories through binning of the predictions, it is shown that for this model class, the use of Mondrian conformal predictive distributions significantly outperforms the use of both standard and normalized conformal predictive distributions with respect to the continuous-ranked probability score. It is further shown that the use of Mondrian conformal predictive distributions results in as tight prediction intervals as produced by normalized conformal regressors, while improving upon the point predictions of the underlying regression forest.