My advice is to start by ‘trying on the hat’ for each business function: Read industry articles from their domain, obtain reports/outputs from their work or have lunch with colleagues from the function to brainstorm ideas. 

As you do this, always consider: 

• Do you speak their ‘lingo’? Different functions will each have their own industry lingo and jargon. The more you speak it, the more you can build their trust. For example, market research folks will appreciate the framing of social media chatter as the ‘voice of the consumer’ for which you can provide both quantitative and qualitative analysis. 
• Can you augment their existing approaches and methodologies? Each function will have existing methodologies and approaches which can be strengthened with social media data. Take market research as an example. Before launch, social media data can inform the (re)design of tracking surveys by identifying ‘unknown unknowns’ topics to be included. It can also be used to better understand consumers’ use of language and terminology, which will help when formulating the questions and answers.
• Can you deliver at the right level of depth, format and frequency? Social chatter can be structured at many different levels; it can be delivered as clean data, information, intelligence, or insight that can tell you the ‘what,’ ‘why,’ the ‘so what’ and the ‘now what’. For instance, some functions, such as analytics teams, may just want an Excel data dump of mentions or sentiment that they can integrate into other data sets. In contrast, CEOs may need a one-page executive summary, with an emphasis on the business implications. 

In considering the above, you are looking at how to structure, package and present social media chatter so that you are answering the right question in the right way at the right depth in the right format and frequency for each business unit. Truth be told, doing this for one additional business function, not to mention for multiple business functions, won’t come easy nor quickly. But I can guarantee you that beginning this process of establishing a Social Media Intelligence Center of Excellence, by extracting more value from the social media intelligence assets, will pay off in the long run, both for your company and your career.