"I've got officials working on shared equity because we know that even the Kiwibuild price brackets are not affordable for lots of people," he said.
"There's no way they could take on a $600,000 mortgage – a $400,000 mortgage, maybe, then you'd get a much bigger group of people."
The shared equity scheme would allow a third party such as a bank or a government agency to co-own a property by taking on a share of the mortgage. That would reduce the owner's deposit and weekly mortgage payments.
The owner could then buy the remaining share off the third party when they could afford to, including any capital gains.
It appears that if the scheme goes ahead, it would be limited to first home buyers on a modest income.
Twyford said one of the key obstacles would be financing the scheme. The Government is in talks with banks about whether they would be interested in putting up capital for it.
Labour's confidence and supply agreement with the Green Party includes a commitment to investigate progressive home ownership models such as shared equity.
The Greens' version of the scheme, which it called rent-to-own, would require participants to make weekly payments of no more than 30 per cent of their income to the Crown, which would co-own the house.
Part of that payment would cover the Crown's costs, and the rest would go into paying off the home. The Greens estimated that the payments would be $100 lower a week than an ordinary mortgage.
Twyford said a shared equity scheme would sit alongside the HomeStart grants introduced by the National Government, which gave first home buyers on modest incomes up to $20,000 towards a deposit.
Those grants had not been effective in Auckland and Queenstown because there were too few houses available below the HomeStart price cap of $650,000.
The consideration of innovative ownership models comes as Labour has been forced to lift its prices for homes built through Kiwibuild.
It had initially promised to build houses for between $500,000 and $600,000. They will now be priced according to the number of bedrooms, and three-bedroom homes will be sold for $650,000 – higher than promised during the election.
National Party housing spokeswoman Judith Collins was critical of the way the Government lifted the Kiwibuild prices, saying today that the higher thresholds had been quietly included in tender documents to developers.
Shared equity schemes have already proven successful in the community housing sector.
One of the largest providers, the NZ Housing Foundation, offers a co-ownership scheme to households earning between $65,000 and $95,000 a year and holds on to 30 per cent of the home.