The phrase "most perambulatory" refers to something or someone that walks or travels a lot or frequently. There are various synonyms for this phrase, including "most ambulatory," "most mobile," "most wandering," "most itinerant," and "most roving." These synonyms describe the same meaning of the phrase, which is the tendency to move or travel from one place to another. Other related synonyms such as "most nomadic" and "most peregrine" also highlight the idea of constant movement or a lack of a permanent home or place. These synonyms can be used interchangeably, depending on the context and preference of the writer or speaker.