The phrase "keeps shoulder to wheel" can be defined as someone who remains dedicated and committed to a task, even if it is difficult or challenging. There are several synonyms that can be used to express the same sentiment, such as "perseveres", "endures", "persistently works", "sticks to it", "remains steadfast", "continues on", "stays the course", "maintains momentum", "never gives up", "doggedly pursues", "resolutely perseveres", and "steadfastly persists". These phrases all convey the idea of working hard and persevering despite obstacles or challenges, as is often required to achieve success and significant accomplishments.