The phrase "degree that" can be replaced with a variety of synonyms to add variety and precision to your writing. Some options include "level at which," "extent to which," "point to which," and "amount to which." Another possibility is to use words like "magnitude," "quantity," or "intensity" in place of "degree" to convey a similar meaning. Depending on the context, you could also use words like "grade," "caliber," or "standard" instead of "degree" to emphasize the quality or superiority of something. Experimenting with synonyms can help you find the perfect word to convey your message with clarity and effectiveness.