Thinking mobile first for existing products is difficult, but not impossible. I believe that product managers of business applications can learn a lot from Airline Website and mobile app designers. Airlines, which have fairly complex websites have created successful web applications by focusing on the core needs of their customers. Banks have done so as well.
I had a chance to see some of these airline apps and listen to experts such as Luke Wroblewski talk about them. I realized that people centricity was a key reason why airlines and banks got mobile apps for their existing websites right. They focused on the things people want to do rather than port all features in the web applications to the mobile phone.
They also thoughts about use cases that one could do only with a mobile phone and not a computer. Depositing a check by taking a picture of the check is a good example of using the unique capabilities of a mobile phone.
Perhaps product managers of business applications should make a pilgrimage to the design studios of Southwest airlines or Chase Manhattan Bank.