I think Blendle is on the right path here, moreso than Medium. They offer a decent uni-branded layout (although I prefer Medium's), but allow tweaks based on the source. I think Apple's News app does the same thing. I can often recognize the source newspaper/magazine despite staying within Blendle's interface (similar to how one could recognize the New Yorker just from the typography).

The one thing I'd like Blendle to add, but maybe they did so already, is the ability to follow journalists. A number of my friends, for example, are freelancers and publish in multiple publications.