When writing or speaking, it's important to vary your language to avoid redundancy and enhance clarity. Instead of repeatedly using the phrase "with the supposition that," consider utilizing synonyms such as "assuming," "presuming," or "postulating." You could also explore phrases like "under the belief that," "with the assumption," or "on the premise" to convey the same idea. If you're looking for a more formal tone, try using language like "given that" or "with the understanding that." By incorporating these synonyms into your vocabulary, you can improve your writing and communication skills.