Both scientists and society at large have rightfully become increasingly concerned about research integrity in recent decades. In response, codes of conduct for research have been developed and elaborated. We show that these codes contain substantial pluralism. First, there is metaphysical pluralism in that codes include values, norms, and virtues. Second, there is axiological pluralism, because there are different categories of values, norms, and virtues: epistemic, moral, professional, social, and legal. Within and between these different categories, norms can be incommensurable or incompatible. Codes of conduct typically do not specify how to handle situations where different norms pull in different directions. We review some attempts to develop an ordering of different sorts of norm violations based on a common measure for their seriousness. We argue that they all fail to give adequate guidance for resolving cases of incommensurable and conflicting norms. We conclude that value pluralism is inherent to codes of conduct in research integrity. The application of codes needs careful reasoning and judgment together with an intellectually humble attitude that acknowledges the inevitability of value pluralism.