News reports about emerging issues often include several conflicting story lines. Individual stories can be conceptualized as samples from an underlying mixture of competing narratives. The automated identification of these distinct narratives from unstructured text is a fundamental yet difficult task in Computational Linguistics since narratives are often intertwined and only implicitly conveyed in text. In this paper, we consider a more feasible proxy task: Identify the distinct sets of aligned story actors responsible for sustaining the issue-specific narratives. Discovering aligned actors, and the groups these alignments create, brings us closer to estimating the narrative that each group represents. With the help of Large Language Models (LLM), we address this task by: (i) Introducing a corpus of text segments rich in narrative content associated with six different current issues; (ii) Introducing a novel two-step graph-based framework that (a) identifies alignments between actors (INCANT) and (b) extracts aligned actor groups using the network structure (TAMPA). Amazon Mechanical Turk evaluations demonstrate the effectiveness of our framework. Across domains, alignment relationships from INCANT are accurate (macro F1 >= 0.75) and actor groups from TAMPA are preferred over 2 non-trivial baseline models (ACC >= 0.75).