The Scottish Premier League is planning a radical overhaul of its own status within Scottish football, including a thorough rebranding and a league reconstruction model involving 24 clubs.

Tomorrow a number of SPL clubs are to meet with Neil Doncaster, the SPL chief executive, to hear the plan. One aim is to counter last week's Scottish Football League proposal of a 16-10-16 model by inviting up to 12 clubs to resign from the SFL and join what is currently the SPL.

The new SPL strategy would create a 24-club elite, involving two top divisions of 12, but under a new corporate banner, with the "SPL" brand being binned.

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"This is not an 'SPL1 & 2'," said an SPL source last night. "The plan is that it would be radical, it would wipe the slate clean. We've had many proposals in recent years, but we hope this might be the one."

The new leagues would involve two top tiers of 12 clubs. A split would come after 22 games, following which the bottom-four clubs and the top four from the second tier would play a further 14 games home and away to determine which four clubs secured top-flight status.

The SPL have looked to various leagues across Europe, and for the 24 clubs it would mean a 36-game league season.

The source added: "Someone referred to it as 'three leagues of eight', as you'd have this battle raging from February onwards in what is effectively an enlarged play-offs system for four spots in the top flight. It is being strongly presented."

If the plan goes ahead it is likely to mean the end of the SPL, at least as a brand. After a summer of upheaval, triggered by the Rangers crisis, some believe the SPL identity is now toxic. A "revamp" is being planned in time for – they hope – a new league sponsor next season.

The clubs hope to have a strategy in place in time for an SPL general meeting on December 3. If successful, the system would be in place for the 2013-14 season.

The plan comes a day after Peter Lawwell, the Celtic chief executive, spoke of the hardship of maintaining a healthy SPL in the current economic climate.

On Friday, Lawwell told the club's AGM that "the landscape of football is changing" and that it is becoming increasingly difficult for Scottish football to remain viable, adding: "We have stability at Celtic, but commercially we are also suffering."

Scottish clubs currently receive less than 1% of the value of Barclays Premier League clubs in terms of TV revenues. "We always need to explore new ideas – you can't stand still," Lawwell said.