Some MPs want the qualifying criteria for a presidential candidate to go beyond the financial and include other strengths as well.
One suggestion is a track record of public service, such as running charities and non-profit organisations.
The revised requirement under the proposed changes to the elected presidency is that private sector candidates must helm a company with at least $500 million in shareholders' equity.
But there is also a "deliberative track" that gives the vetting body, the Presidential Elections Committee, some flexibility in deciding who qualifies to stand for election.
These include chief executives of companies limited by guarantee, or managing partners of large partnerships, or chief operating officers of exceptionally complex companies.
THE DEBATE: Why president should be elected
It is clear to me, Madam, that the president should remain an elected office and his Council of Presidential Advisers (left) should be appointed. Singaporeans have been accustomed to this since 1991. We should not go back in time and extinguish their right to vote for a head of state who is empowered, in specific circumstances, to veto the Government if it is necessary to do so.
NOMINATED MP MAHDEV MOHAN
The MPs also called for greater transparency in the decision-making process on whether candidates meet the criteria.
In calling for an expansion of the criteria, Mr Zaqy Mohamad (Chua Chu Kang GRC) said: "The president is not applying to be chairman of a listed company, in which his financial and corporate track record should be the key criteria for evaluation."
TRACK RECORD MATTERS
He is applying to be the president of Singapore - a role that demands a track record of service to society, of demonstrated ability and willingness to have contributed to society and Singaporeans, in a leading role, in addition to his role as custodian of Singapore's reserves. ''
MR ZAQY MOHAMAD (Chua Chu Kang GRC), calling for broader eligibility criteria for candidates
HIGHER BAR JUSTIFIED
Far from being elitist, in fact we should make no apology for wanting the bar to be set higher to ensure that everyone aspiring to that position will be well qualified. And really, why should we accept any less when the issues at stake are our reserves, which represent our future and our children's future? ''
MR EDWIN TONG (Marine Parade GRC), on the more stringent eligibility criteria for candidates
PEOPLE SECTOR LEADERS
The people sector may currently be small and not as steeped in power, organisational sophistication and financial resources, but neither should it be seen as a lesser brother to the public and private sectors. It is a vital part of the equation in the total defence of our country and the guardianship of our national unity and it deserves equal respect.
NOMINATED MP KUIK SHIAO-YIN, suggesting the Presidential Elections Committee and Council of Presidential Advisers include people sector leaders
Instead, the president's role demands a track record of service and willingness to contribute to society, in addition to being a custodian of the national reserves, he said.
Mr Zaqy suggested adding "softer" criteria such as leading a charity or non-profit organisation.
"The gauge to measure the president must be broader and not narrower," he added.
Mr Christopher De Souza (Holland-Bukit Timah GRC) said the "deliberative track" has to be broad enough to include the first four presidents: Mr Yusof Ishak, Dr Benjamin Henry Sheares, Mr Devan Nair and Mr Wee Kim Wee.
They contributed immensely to Singapore before they were appointed, but "they neither ran $500 million companies nor did they occupy an office that would immediately qualify them to even stand for election", he said.
While the financial criteria are useful to the office of the president, they are not everything, he said. "It cannot be all about commerce."
The candidate has to be "people-centred, community-centred and nation-centred", said Mr De Souza, sharing Mr Zaqy's view that presidential candidates should hold leadership positions in charities and non-profit organisations.
Nominated MP Kuik Shiao-Yin said that "people sector leaders" such as social workers who help broken families should also be considered.
"This is not about simplistically asking for people sector leaders to be given an easier shot at running for the presidency," she said. Rather, such candidates with social experience can unify the country.
But whatever the criteria, they cannot be so strict that they create an "empathy gap" between political leaders and the electorate, she said.
Two MPs suggested using the National Day Awards as a yardstick.
"Would recipients of the nation's highest orders and decorations - such as the Order of Temasek or the Order of Nila Utama - and who may not automatically qualify, also be deemed to qualify?" asked Nominated MP Mahdev Mohan.
Mr De Souza noted that top National Day awards such as the Distinguished Service Order are given to those who have distinguished themselves and made significant contributions to Singapore. Using such awards will allow the committee to understand the "comparable contributions" across candidates, he said.