He said the encouraging results and "ongoing demand from sponsors and communities" had prompted the third round of applications.
Partnership, or charter, schools were part of Act's confidence and supply agreement with National.
Since the first five opened in 2013, one has had to be bailed out by the government with extra cash and support after it was found to be failing almost all the benchmarks in its contract.
During a special review auditors found Te Pumanawa o te Wairua, in Northland, had poor financial controls, and it was unable to provide key financial information such as operational budgets, forecasts and management reports. It also had a litany of academic and governance failings. Education minister Hekia Parata decided to keep it open with another review at the end of the year.
Other schools have been criticised for high funding rates, failure to recognise Maori culture properly and a an inability to meet roll criteria.
Labour's education spokesman Chris Hipkins slammed the decision to open more schools was " throwing good money after bad".
"There are already major problems with several of the first charter schools that haven't been addressed. Why on earth plough ahead with opening more schools when there have been so many problems with the ones already operating?" Mr Hipkins said.
"The whole charter school process has been flawed from day one. Their establishment has been rushed, the due diligence that would normally happen before a new school is opened hasn't been completed, and major problems have inevitably followed.
He said minor tweaks to the funding model won't address the real issues.
PPTA President Angela Roberts said the government was "scrabbling" to save a failing policy.
"The exorbitant amounts that some of the charter school operators are banking as surpluses or paying themselves as 'management fees' obviously has the Minister alarmed," Ms Roberts said.
"We were told that this policy was a pilot, which would be rigorously evaluated," said Roberts.
"The evaluation hasn't reported anything yet, but here we have more charters being announced, and the policy being changed already."
She said it was a "shambolic" way to make policy.
In a release, Mr Seymour said the funding changes would reduces establishment costs, and emphasise 'per-student' funding.
He said when Partnership Schools reach maximum roll, they will receive funding broadly the same as the state school.
Other changes would allow for establishment and operating issues to be dealt with more easily as they arise.
