We all know the concept of the Peter Principle: All good managers eventually get promoted to one level above their ability. My work with thousands of business leaders has led me to another, more nuanced conclusion: Every business leader will at some point in their career face a challenge they are constitutionally incapable of solving—sometimes with career-ending results.

All leaders fall into one of three natural leadership styles: the Visionary (strategic, creative, charismatic, communicative, committed to step change); the Operator (driven, tactical, focused, determined, ruthless); and the Processor (process oriented, systems focused, iterative, conservative, risk averse, pensive).

When there is a clear match between the leader’s style and the challenge he or she faces, all is good: Steve Jobs in his later years, for example, was a true Visionary, leading Apple back from the brink; Warren Buffett in his early years was a genial Processor, relentlessly scouring data in order to eke out incremental growth for Berkshire Hathaway; and Herb Kelleher used charm and geniality to mask his ruthless, Operator-driven leadership of Southwest Airlines in its early, fast-growth phase.

The problem comes when a leader faces (or is thrown into) a challenge that falls outside their natural style. Think of two leaders who have conspicuously failed to move the needle in recent years: Vikram Pandit, a natural Processor, repeatedly and furiously tinkering with the structural minutiae of Citibank; or Steve Ballmer, an über-Operator trying to grow Microsoft by dint of sheer effort and willpower. Why have they failed? Because what both companies need more than anything right now is a Visionary.

Conversely, look at the fates of renowned office decorator John Thain at Merrill Lynch and the perennially flush-faced Ken Lewis at Bank of America, a Visionary and an Operator, respectively, both of whom found themselves beached when the environment shifted, leaving their companies desperately in need of a more risk-averse, steady-as-she-goes Processor. Or Leo Apotheker at HP, a dyed-in-the-wool Processor who felt pressured to act like a Visionary during his short stint at the company, producing as a result one of the most derided, misbegotten strategic plans any public company has come up with in recent years.

The tech industry has its own wrinkle (as always): the brilliant Processor who everyone thinks is a Visionary. Jerry Yang finally accepted his "non-V-ness" in recent weeks and stepped away from Yahoo years after his Processor contributions ceased to be helpful. Larry Page is a walking case study in "brilliant P masquerading as V," and recent moves by Google under his leadership (such as the acquisition of Motorola Mobility) seem to confirm that a genius Processor may walk and talk and look like a Visionary, but that doesn’t mean he or she is one.

So, what’s the answer? Are corporations destined to switch leaders every few years as the nature of the challenge they face changes? Not necessarily. Though, as a strategy, is beats leaving a beached V, O, or P in place long past their time of optimum contribution.

Truly great leaders learn—eventually, and usually at the school of hard knocks—to transcend their V-, O-, or P-ness. Remaining Visionaries, Operators, or Processors at their core, they develop over time a fourth, learned style—one I have come to call the “Synergist.”

Synergists can and do use their “natural” Visionary, Operator, or Processor skills at any time, but they aren’t limited or constrained by them. Nor are Synergists blindsided when faced by challenges that go beyond their natural style. Steve Jobs—a naturally strong V—came back to Apple after exile as a Synergist-Visionary and proceeded to build an enormously successful company that will long outlive him. After Buffett grew his business as large as he could, he learned to become a Synergist-Processor, and he now makes Visionary deals that he never would have contemplated in his early years.

Bill Gates (a natural Processor) became a great Synergist through his philanthropic activities in later life, but too late for Microsoft. The early “Neutron” Jack Welch was an Operator-Processor (as many engineers are), but as he learned to grapple with the complexities and nuances of leadership, he gradually transformed into an exceptional Synergist.

Sadly, not every business leader makes the transition. Howard Schultz appears to have remained a staunchly nonsynergized Visionary, and Starbucks is likely to lose its mojo when he inevitably and eventually has to step down. Steve Ballmer resolutely refuses to either understand or appreciate the Synergistic aspect of leadership and seems fatally determined to turn Microsoft around on Operator bluster alone. HP’s board continues to hop from V to O to P (Carly Fiorina, Mark Hurd, and Apotheker, respectively) without seeming to be aware there is a better, fourth option.

What’s your leadership style? Are you naturally a Visionary, an Operator, or a Processor? And have you made the transition yet to being a Synergist? Find out in this free quiz.