The crunch meeting in New York follows the failure earlier this week of George Shaheen, head of the worldwide Andersen Consulting business, to secure the two-thirds majority necessary to succeed Larry Weinbach, who stands down as head of the Chicago-based firm later this year. The blow comes just weeks after the 2,700 partners turned down the board's recommendation of Jim Wadia, head of the UK operation of the Arthur Andersen accountancy firm.
Since the 27-strong board drawn from all parts of the organisation has used up both its candidates, nobody is willing to predict the outcome of a gathering scheduled to run into tomorrow. "We're in uncharted waters," one insider said.
Trying to persuade Mr Weinbach, an architect of the original split, to stay on is one option. But it is thought that Mr Weinbach, who is reportedly keen to pursue other interests outside the firm after eight years at the top, will take some convincing.
The firm is seeking to play down suggestions that the impasse results from tensions between the two arms of the organisation by pointing out that both men had secured simple majorities - though not the required "super majority" - in the polls.
However, some outsiders believe the problems are connected to a lengthy review of the future organisation of the firm, which employs more than 100,000 people around the world and last year achieved revenues of $9.5bn (pounds 5.7bn), almost exactly equally split between the two units.
At a meeting in Paris earlier this year, the partners voted overwhelmingly against a more complete split between the accountancy firm and the consulting operation, which was hived off in 1989. But it is known that some in the firm are irritated that the consulting arm, which has become associated with large-scale information technology and outsourcing projects, increasingly finds itself competing for business against consultants from the accountancy arm.
Other observers, though, believe the troubles may be more territorial and stem from partners in the United States earning more than their colleagues elsewhere in the world.
Either way, the long-running and well-publicised troubles leave the normally coolly efficient Andersen open to accusations that it cannot be taken seriously as a business adviser if it cannot even choose its own chief executive.
One insider admitted that the saga was bound to be closely followed by other big six accountancy firms that have long envied Andersen's apparent effortless ability to grow strongly even at times of recession, but was not concerning clients.
A spokesman for another leading firm of accountants and consultants said that the firm was paying the price for adopting a simple form of democracy. Mr Weinbach believes that though an election involving such a large and spread-out electorate is "a difficult and demanding process", it makes a new chief executive assured of the support of the other partners.
At most other partnerships, senior partners simply emerge from gatherings of senior managers. Hitherto, it has been inconceivable that partners in a successful professional services firm would reject the recommendation of the management on such an important issue once, let alone twice.Reuse content