Recent advances in text summarization have predominantly leveraged large language models to generate concise summaries. However, language models often do not maintain long-term discourse structure, especially in news articles, where organizational flow significantly influences reader engagement. We introduce a novel approach to integrating discourse structure into summarization processes, focusing specifically on news articles across various media. We present a novel summarization dataset where news articles are summarized multiple times in different ways across different social media platforms (e.g. LinkedIn, Facebook, etc.). We develop a novel news discourse schema to describe summarization structures and a novel algorithm, DiscoSum, which employs beam search technique for structure-aware summarization, enabling the transformation of news stories to meet different stylistic and structural demands. Both human and automatic evaluation results demonstrate the efficacy of our approach in maintaining narrative fidelity and meeting structural requirements.