in an insatiable manner; with persistence but without satisfaction; "he clawed insatiably at the traditional precepts" to an insatiable degree; "she was insatiably hungry
If someone has an insatiable desire for something, they want as much of it as they can possibly get. The public has an insatiable appetite for stories about the famous = voracious. always wanting more and more of something insatiable appetite/desire/demand etc (for sth) (insatiabilis, from satiare )