EdgeR condition-specific dispersion

[tfwillems]

I'm dealing with a factorial RNA-seq data set in which cells have been stimulated with various combinations of extra-cellular cues. As such, I was interested in applying the GLM framework in edgeR to assess the contribution of each extra-cellular cue to the differential expression of certain genes. My concern, however, is that both the expression level and the dispersion of each gene varies greatly with the combination of cues. EdgeR doesn't seem to estimate condition-specific dispersion but rather one dispersion per gene (if the tagwise options is used). My question is therefore two-fold:
1) Does it make sense to want to estimate condition-specific dispersions?
2) Is there a way to modify the edgeR framework so that it does this?

[tfwillems]

Thanks to Mark Robinson and Gordon Smyth for answering this