Disengaged responding poses a severe threat to the validity of educational large-scale assessments, because item responses from unmotivated test-takers do not reflect their actual ability. Existing identification approaches rely primarily on item response times, which bears the risk of misclassifying fast engaged or slow disengaged responses. Process data with its rich pool of additional information on the test-taking process could thus be used to improve existing identification approaches. In this study, three process data variables--text reread, item revisit, and answer change--were introduced as potential indicators of response engagement for multiple-choice items in a reading comprehension test. An extended latent class item response model for disengaged responding was developed by including the three new indicators as additional predictors of response engagement. In a sample of 1,932 German university students, the extended model indicated a better model fit than the baseline model, which included item response time as only indicator of response engagement. In the extended model, both item response time and text reread were significant predictors of response engagement. However, graphical analyses revealed no systematic differences in the item and person parameter estimation or item response classification between the models. These results suggest only a marginal improvement of the identification of disengaged responding by the new indicators. Implications of these results for future research on disengaged responding with process data are discussed.