To a higher degree is a phrase that indicates an increase in intensity or level. There are several synonyms that portray the same meaning, including 'to a greater extent,' 'more significantly,' and 'more profoundly.' 'To an elevated level' and 'to an enhanced degree' are also common synonyms used to express a more intense or greater level of something. 'To a heightened degree' is another example that denotes an increased level of intensity. Additionally, 'to a maximal extent' can be used to describe something that has reached its highest level. In conclusion, there are numerous synonyms that can be used interchangeably with 'to a higher degree' depending on the context.