I think it would be possible to follow the example of the other commissioner, the Privacy Commissioner of Canada.
Privacy commissioners have not been shy about conducting studies, issuing reports, and commenting on the privacy practices of government entities and, indeed, private sector firms. I think it's entirely possible to give a specific mandate to the transparency commissioner to conduct ongoing studies and make recommendations on the continuing improvement of transparency practices.
My view is that it should cover the entire federal public sector, not just the executive branch departments and agencies but also all Crown corporations, Parliament itself and the courts, all of which are part of our system of governance.