"about the premise" is a correct and usable phrase in written English.
For example, "John was skeptical about the premise of the argument."
But what about the premise, what about modern art?
That said, something about the premise and structure of this book feels off.
My complaint is about the premise of the article, which you did not address.
In fact there is nothing the least bit plausible about the premise of mistaken identity served up in this novel.
For me that's the only really contentious thing about the premise of the show, ie cash for kids.
But there has been little dispute about the premise that psychologists have extrapolated from an outlying few the ways of the global many.
It is these mechanical wonders, scattered about the premises, that make the storefront so remarkable on the rural highway.
Many of the animals are displayed in barless, moated enclosures, while a colony of lion-tailed macaques is allowed to move freely about the premises.
You'd be better off with me if you asked those questions about the premises in the question you want to ask".
Avoiding spoilers, let's say that the resulting contrast — between the committee's depiction of the events and Eastwood's own — turns "Sully" into a film about itself, a movie about the premises and powers of movie-making.
In communities of color, the foreclosed houses "were more likely to have trash strewn about the premises, overgrown grass, shrubbery, and weeds, and boarded or broken doors and windows".
