Here, I introduce a transformation-based method for extending the Baum-Welch algorithm to the training of discrete Hidden Markov Models subject to constraints on the parameters. A class of certain linear factorial constraints is described and shown to lead to exact reestimation formulas. Applying these constraints to the hidden state transitions allows to estimate processes that are cartesian products of multiple sub-processes on differing timescales. The applicability of the method has been demonstrated previously using constraints on both hidden and observation processes. The potential benefit of the approach is discussed in qualitative comparison to factorial Hidden Markov Model architectures.