When it comes to describing an inexpugnable desire, there are many synonyms that can be used. Some of the most common options include unshakeable, irresistible, insatiable, and unquenchable. Other synonyms that can be used to convey a similar sentiment include overwhelming, intense, fervent, burning, and passionate. Each of these words can be used to describe a strong and unwavering desire, and can be used to describe everything from a craving for something as simple as food or drink to a desire for love, success, or personal fulfillment. Whether you're trying to describe your own inexpugnable desire or exploring the concept in literature or art, these powerful synonyms can help you convey the depth and intensity of your feelings.