Ten clubs sent their proposal to the Scottish Premier League following a meeting at Hamilton's New Douglas Park on Thursday night.
Second-tier clubs fear for their ability to sustain full-time football after the collapse of a plan for a new merged body, which was vetoed by Ross County and St Mirren at an SPL meeting last month.
Hamilton chairman Les Gray on Friday night confirmed they had grown frustrated with the Scottish Football League board and the rebel group hope the SPL will meet them to discuss a two-tier structure.
Gray would not go into details of their proposal to the SPL, whose clubs are due to meet on Tuesday at a second meeting to discuss introducing play-offs as an alternative to the failed plan to split the top two tiers into three divisions after 22 games.
But he told BBC Radio Scotland: "We have always said we would prefer a 42-club solution. If they are unable to do that, we can't sit on our hands and see what happens. We have given them (SPL) an alternative and that option includes a second tier, a Championship. That's all there is to it, there is nothing sinister behind this. There were 10 clubs at the meeting who were all in agreement to put this proposal. I'm not going to name them."
First Division clubs were the biggest losers when the SPL rejected the proposals, which were designed to create extra revenue to spread among their ranks.
Gray added: "I have spoken to the SPL chairman over this and I have always felt there was some warmth towards the idea of a second tier, but it has never got over the line. We are going at it from the angle that this is the last chance to do something for next season and there is a will to do it.
"There are clubs in danger, there are clubs having to consider part-time, and there are jobs in danger. We need to try to get this through so that we can create extra wealth for that second tier."
The SPL confirmed they would discuss the proposal.