Written down Cantonese and Mandarin are mutually intelligible. They have regional grammar and vocabulary, but not excessively so. They're mostly pronouncing words differently
Perhaps you could say there's a subset of the languages which can be mostly written in a mutually intelligible way. That sounds more like the similarities between, say, Portuguese and Spanish, though, where you can probably write a subset of the languages that is pretty comprehensible by both language speakers, yet the languages are distinct.