The SPFL have written to all 42 clubs asking for their views on a proposed permanent move to a 14-10-10-10 league restructure.
An "indicative vote" is being requested from all clubs by Monday June 15 at 10am with the intention of the structure, if successful, being put in place from next season.
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The proposal would not only mean altering the current financial distribution model but also admitting two new member clubs from the Highland and Lowland Leagues.
Any such move would need the support of 11 of the 12 Premiership clubs as well as 17 or more clubs from the Premiership and Championship combined and 32 or more overall.
Neil Doncaster, chief executive of the SPFL said: "It is clear there is enough support for a permanent 14-10-10-10 structure to merit a second consultation stage.
"It's important to underline this is not a binding vote and is intended only to steer the board on whether to put forward a formal resolution for voting on, or not."
If there is sufficient support, any required EGM would have to be held within seven days due to the tight timescales involved in confirming fixtures for the start of the 2020-21 season in August.
The SPFL admit there is sympathy for the clubs relegated due to the curtailment of the current season due to the coronavirus pandemic with this proposal meaning those teams would immediately regain their previous divisional status.
Such a reconstruction would also see the second-placed teams in the Championship, League 1 and League 2 (Inverness Caledonian Thistle, Falkirk and Edinburgh City) promoted as well as the aforementioned promotion into League 2 of a team from each of the Highland and Lowland Leagues.
However, the SPFL are quick to point out no other league reconstruction proposal would be considered after both Rangers and Hearts had previously put forward their own plans.
And should the results of the indicative vote show there is insufficient support for a 14-10-10-10 structure, the existing League structure will be maintained.
'We shouldn't rush reconstruction proposals'
Ross County chairman Roy MacGregor believes the issue of league reconstruction shouldn't be rushed through with the immediate focus instead being on the new season and the challenges surrounding it.
"Clubs should only be concentrating at the moment on getting training back, to get contact training back, and to get matches going," MacGregor said.
"We only have maybe seven weeks until the start of the season, so to think of reconstruction at a time when the Scottish football environment has been stressed is the wrong time.
"But I do think that it should something that should be considered, we should take our time with it, and we should examine it thoroughly."