From Longman Dictionary of Contemporary Englishplough on phrasal verbCONTINUE/NOT STOPto continue doing something that is difficult or boring with Julia ploughed on with the endless exam papers. He looked displeased but she ploughed on regardless. → plough→ See Verb table
Examples from the Corpus
plough with• Mr Sugar is ploughing on with the rationalisation announced last year.• But live these experiments are virtually forgotten as they plough on with their ridiculously outdated, clichéd brand of power punk. 