Treat it like an investigation with answering these types of questions:

1. What are the problems with the company that you’re interviewing with trying to solve?

2. What are the anticipated outcomes of these problems and what is the timeframe to achieve those?

3. How would you approach solving these given your experience (or if not experienced, your approach to solving any problem in the past).  And I’m referring to a systematic, thought provoking process, not just “Googling” for an answer.

The more you can find out about #1 and #2 before the interview, the better. Then further flush these out during the interview. Then write a short follow up afterwards summarizing what you heard and your approach. 

Will it guarantee a new position? Of course not. 

Will it help you stand out and be remembered? Without a doubt.

Will it help you be better prepared for your next interview? 100%

In Summary: Investigate, Anticipate, Demonstrate, Correlate, Collaborate, Differentiate, Be Great!