A mystery candidate became the third member to submit the 50 signatures needed to challenge the incumbent directors. Nationwide said it would not reveal the member's identity because the member had not sought publicity.
Two other candidates, Andrew Muir and Michael Hardern, are running for director despite having no experience in building societies or banks. The deadline for members to submit nominations is today.
Mr Muir, a 32-year-old recruitment consultant from Slough, will today send the Nationwide a fresh resolution asking the society to highlight ways to reward account-holders. But he will stop short of demanding the society floats on the stock market.
Mr Muir, who runs a small recruitment consultancy called Accountancy Support, has withdrawn an earlier resolution which proposed a windfall of at least pounds 500 each to members - without floating the company on the stock market.
"A third of members wanted conversion last year. A third is a big majority. Yes, it's not the whole majority, but you can't just wipe them under the carpet," Mr Muir said.
Nationwide struck out Mr Muir's first resolution, saying it appeared to show he did not understand the way building societies worked. If Nationwide had 4.5 million eligible members who received pounds 500 each, this would reduce the society's pounds 2.2bn reserve to nothing, making business impossible. "Effectively suggesting we have no reserves is not a viable suggestion," said a spokesman for Nationwide.
Mr Hardern was defeated in his bid to be elected to the board last year by a two-thirds majority. A butler by profession, he is running again in an effort to force a vote on conversion.