SPL chairman Lex Gold described the move as "seismic" and said the restructuring would be good for top-flight football in Scotland.
A meeting of the present 12 SPL clubs also approved the introduction of a cup tournament restricted to member clubs.
Require clubs to "demonstrate current best practice in corporate governance".
Any club wishing to leave the SFL must serve two years notice, unless 20 of the 30 clubs that make up Divisions One, Two and Three support the change.
But Gold insisted nothing will be confirmed without consultation with other governing bodies.
Our clubs decided it would be of interest to Scottish football to invite 10 further clubs to join a restructured top flight
"The general motivation for our clubs has been to see if we can strengthen the top structure of the game in Scotland," he said.
"They decided it would be of interest to Scottish football to invite 10 further clubs to join a restructured top flight.
"We are going to be discussing that, in the first instance, with our colleagues in the Scottish Football League and with the Scottish Football Association.
"Our clubs also had a look at the paper produced by nine of the 10 First Division clubs and broadly support the pyramid structure."
The proposal, championed by Livingston chairman Pearse Flynn but not yet supported by Gretna, suggests that the remaining clubs below the SFL should form regional leagues.
"Also, in relation to regionalisation, they believe this could serve as a catalyst for further thought to be given to that," said Gold.
"But they were also clear that is not a matter for our clubs but for the SFL and the SFA.
"With a change of this nature, you have to be sensitive to it, hence our decision to have discussions with our colleagues at the SFL and the SFA."
At present, the three Scottish Football Leagues below the SPL are without a sponsor and do not have regular television coverage.
But one First Division club owner told BBC Sport that a major international gaming company was lined up to sponsor both the current SPL and the new "SPL Two".