The REACH legislation of the EU requires that transformation products be included in chemicals assessment for chemicals produced or imported in amounts exceeding 100 tonnes/year. However, including transformation products in assessments could be considered an intractable problem, particularly given the paucity of available data and the difficulty of predicting the most likely transformation route from the many possible products of a complex parent chemical (the so-called "combinatorial explosion" problem). Here, we present a scheme for identifying transformation products that substantially contribute to the joint persistence of a parent chemical and its substance family. Our scheme integrates methods for the prediction of biodegradation products, the estimation of physicochemical properties and degradation half-lives, and the calculation of a persistence metric, the joint persistence. We compare results from our scheme to 22 test cases with known transformation products. Our results highlight that the "combinatorial explosion" problem can be managed but that there is a serious need for better data for environmental half-lives of chemicals.