There are numerous synonyms for the phrase "suggest itself". Some of the most common alternatives include "come to mind", "occur to", "present itself", "be suggested", "strike", "pop up", "appear", "arise", "suggest", "cross one's mind", and "occur". All of these synonyms convey the idea of an idea or suggestion coming into one's consciousness or consideration without conscious effort or deliberate thought. They can be used interchangeably in most contexts to add variety or nuance to one's writing or conversation, and to emphasize the spontaneous and organic nature of the idea or suggestion in question.