"But that will be years away and there'd have to be demonstrably no progress ... I doubt very much we'd get to that situation but if we had to get [to] that point we would do it," he said.
Simplicity has close to 6700 members and $175 million funds under management and Stubbs said if that level of growth continued the provider would become a "reasonably large shareholder" of these firms within five years.
"We would have some sway or influence all by ourselves but I'd be surprised if we wouldn't get other shareholders rallying around if it became obvious that nothing was happening," he said.
Stubbs said a growing amount of research showed that companies with more diverse management were outperforming their less diverse counterparts.
He said it was not up to Simplicity to explain to companies what improved diversity would look like - whether across gender, ethnicity or age.
"But it will be obvious when you see photos of the board and management when it's been achieved," he said.
AUT University research from earlier this year found that only 4 per cent of the NZX 50's chief executives or chairpersons were women and even fewer were Maori, Polynesian or Asian.
That research examined the board makeup of the stock exchange's 100 biggest companies and found that 22.17 per cent of their directors were women. That was up from 8.65 per cent in 2008.
The research, by AUT's Judy McGregor and Stevie Sikuea, found that six of these companies had an equal number of female and male directors but that 25 still had no women on their boards.
YWCA chief executive Monica Briggs supported Simplicity's initiative and said the five-year time-frame was reasonable.
Having a publicly available scorecard on diversity was going to put pressure on firms, she said.
"We do need some urgency around this now ... there are a lot of women which are board ready. I think five years is do-able and that New Zealand is starting to lag behind [other countries]," Briggs said.
While diversity was the first issue on Simplicity's radar, Stubbs said the KiwiSaver provider could also look to drive a debate about whether companies were paying out too much in dividends instead of reinvesting profits for growth.