"Based on assumption that" is a phrase often used to convey a hypothetical or speculative situation. However, there are other ways to express this idea using synonyms such as "presuming," "assuming," "supposing," "implying," or "inferring." These words suggest a scenario where a conclusion has been drawn based on limited information or speculation. Furthermore, phrases like "with the understanding that," "given that," and "in light of" indicate that a particular idea or outcome is likely or probable, but not necessarily a certainty. In summary, there are many synonyms for "based on assumption that," each highlighting the uncertainty and speculation that accompanies such a statement.