Most rivalrous refers to something that is highly contested or fiercely competitive. Synonyms for this term could include words such as contentious, combative, aggressive, antagonistic, and cut-throat. Other words that could be used to describe a highly competitive situation might include words like challenging, intense, cutthroat, or dog-eat-dog. In some cases, it might also be appropriate to use words like fierce, competitive, or adversarial to describe a situation that is marked by intense rivalry or competition. Ultimately, the choice of synonym will depend on the context in which the term is being used, as well as the intended tone of the writing or conversation.