Language acquisition depends on the ability to detect and track the distributional properties of speech. Successful acquisition also necessitates detecting changes in those properties, which can occur when the learner encounters different speakers, topics, dialects, or languages. When encountering multiple speech streams with different underlying statistics but overlapping features, how do infants keep track of the properties of each speech stream separately? In four experiments, we tested whether 8-month-old monolingual infants (N = 144) can track the underlying statistics of two artificial speech streams that share a portion of their syllables. We first presented each stream individually. We then presented the two speech streams in sequence, without contextual cues signaling the different speech streams, and subsequently added pitch and accent cues to help learners track each stream separately. The results reveal that monolingual infants experience difficulty tracking the statistical regularities in two speech streams presented sequentially, even when provided with contextual cues intended to facilitate separation of the speech streams. We discuss the implications of our findings for understanding how infants learn and separate the input when confronted with multiple statistical structures.