Rapid response latencies in conversation suggest that responders start planning before the ongoing turn is finished. Indeed, an earlier EEG study suggests that listeners start planning their responses to questions as soon as they can (Bögels et al., 2015a). The present study aimed to (1) replicate this early planning effect and (2) investigate whether such early response planning incurs a cost on participants' concurrent comprehension of the ongoing turn. During the experiment participants answered questions from a confederate partner. To address aim (1), the questions were designed such that response planning could start either early or late in the turn. Our results largely replicate Bögels et al. (2015a), showing a large positive ERP effect and an oscillatory alpha/beta reduction right after participants could have first started planning their verbal response, again suggesting an early start of response planning. To address aim (2), the confederate's questions also contained either an expected word or an unexpected one to elicit a differential N400 effect, either before or after the start of response planning. We hypothesized an attenuated N400 effect after response planning had started. In contrast, the N400 effects before and after planning did not differ. There was, however, a positive correlation between participants' response time and their N400 effect size after planning had started; quick responders showed a smaller N400 effect, suggesting reduced attention to comprehension and possibly reduced anticipatory processing. We conclude that early response planning can indeed impact comprehension processing.