That's what Alyson points out so well in the article, The Case For Embracing Lateral Career Moves, published by FastCompany. If you assume, as so many do, that exponential or total change of your skill set is required, then the prospect of reinvention is daunting. During the worst of the recent great recession, many who lost their jobs appeared to be like a deer in headlights, because they didn't understand those possibilities. If, however, you understand that reinvention can be incremental, by changing perhaps a few skills, with the result that a new skill set is created, then the prospect seems more readily achievable. There are numerous people who have done just that.
In my book Invent Reinvent Thrive (McGraw Hill, 2014), I relate some of their stories and explain why such reinvention is critical and how incremental reinvention is readily achievable. The stories include (i) a soldier, who became a businessman, then a venture capitalist and a philanthropist and ultimately the Mayor of Jerusalem; (ii) a grocer who understood retail but not the office products industry but who sharpened a few skills to fit that industry and founded Staples; (iii) a solo practicing physician who ultimately became the president of the largest group of physicians in Illinois; (iv) a man who considers himself a failure in school, who first toyed with using computers in his father's car dealership, who then tried his hand at selling computers and related products that he obtained at reasonable cost from others who didn't know what to do with such inventory, finally founding CDW which he sold for billions.
As Alyson points out in her article, it doesn't matter whether you adjust your skills through multiple jobs at different employers or by lateral shifts within the same company. Either way, refining your skill set by refining or changing just a few skills generally is sufficient to achieve a meaningful reinvention.