Recent research has sought to examine how learners are able to track the co-occurrence of words and objects across moments in time, a behavior commonly termed cross-situational statistical learning. The current experiment was designed to examine if learners can simultaneously determine word-referent pairings while engaging in other cognitive processes that support language learning, such as distinguishing phonologically overlapping words. Participants were presented with a cross-situational statistical learning task with pairs of words in four categories: non-minimal pairs, near minimal pairs, vowel minimal pairs, and consonant minimal pairs. The results revealed that participants were able to simultaneously learn word-referent pairings while distinguishing all four categories of word pairings. However, learners experienced the most difficulty learning vowel minimal pairs. This work demonstrates that learners are able to simultaneously engage in multiple cognitive processes that support language learning.