When modeling genetic regulatory interactions, it is often assumed that the mRNA expression of a transcription factor is a reliable proxy for the regulatory activity of that transcription factor. There are many examples where this assumption does not hold due to post-transcriptional and translational modifications of the transcription factor protein. As true transcription factor activity is very difficult to measure, methods to infer it are becoming increasingly common and it is likely that will become increasingly important when building models of regulatory interactions. Previously, we have shown how Bayesian techniques, particularly Markov- Chain Monte-Carlo based sampling, can enable us to make inferences regarding the activity of transcription factors based on the transcript levels of their targets. However, in that work, we only looked at simple regulatory interactions where one transcription factor acted individually on a set of target genes. In this work, we investigate extending this model to the more general (and common) case of multiple transcription factors working together. As an example application, we use data from a small regulatory network from the fission yeast cell cycle in which several transcription factors are known to work together to produce the desired response, and for which plentiful experimental data are available.