There are several synonyms that can be used for the phrase "got on with it." These include "proceeded," "continued," "carried on," "pushed through," "persevered," "kept going," "sustained," and "maintained progress." Each of these words suggests a sense of determination and focused effort towards completing a task or achieving a goal. Whether it is in the workplace, at school, or in personal life, having the ability to "get on with it" is a valuable skill. By using these synonyms, one can convey a sense of purpose and diligence in their actions while also lending variety and nuance to their language.