Scottish Professional Football League chief executive Neil Doncaster senses clubs will be open-minded about potential reconstruction and sympathetic to the plight of relegated clubs.
One of the clubs who face dropping down a division after the season was curtailed by the coronavirus pandemic, Hearts, are aiming to revive plans to reform the divisions after a number of their top-flight rivals appeared to rule out any prospect of change this summer.
Owner Ann Budge is working on a plan which would need at least nine and probably 11 Premiership clubs to agree and the last attempts at league reconstruction in Scotland, in 2013, failed to get enough support.
"Ann Budge of Hearts is keen to come back again with another resolution looking at reconstruction around an enlarged Premiership," Doncaster told Sky Sports News.
"Clearly that would have the consequence of effectively avoiding relegation for those clubs relegated as a result of the early curtailment of season 19-20.
"Any change would certainly need to go to a vote and it really depends what form of process Hearts choose to go down.
"We have members' resolutions, board resolutions, possible potential for an EGM, and I know that we, at the centre, will be doing what we can to support those efforts and it will remain to be seen whether they are supported by member clubs in the numbers that are required.
"It is likely that any expansion would need 11 out of the 12 Premiership clubs to approve it and 75 per cent effectively of other clubs. But it does depend on the detail.
"But we are certainly looking forward to seeing the proposal and, as and when we receive it, we can share it with member clubs and have a broader discussion.
"It's something that a number of clubs have said they are open-minded about and I think there is a sympathy for the position that the relegated clubs find themselves in and we'll see where it goes.
"We await the proposal and I know that a lot of clubs will want to look at it with a really open mind."
However, sympathy was in short supply from one of the key individuals of Hearts' relegation rivals, St Mirren.
Hearts could have got off the bottom of the Premiership less than 48 hours before the league was suspended but they went down to a limp 1-0 defeat in Paisley.
And Buddies chief executive Tony Fitzpatrick told the Paisley Daily Express: "I have to stress this is my opinion and not the opinion of the club, but Hearts do deserve to go down.
"They've played 30 games and only managed four or five wins, so as far as I'm concerned they are bottom of the table for a reason.
"They had money available and made some big signings in the January transfer window but results still weren't going their way and, to be honest, I couldn't see that changing for them."
Budge has threatened legal action if her plans do not succeed but Doncaster reiterated that all clubs could suffer in that scenario.
"I think it's very important that any club makes its own decisions because they are an independent business," he said. "Although they are one of 42 clubs within the league, each club and each board of each club has to do what's right for their club.
"But as I have said previously, any action that is taken by any member against the league is ultimately taken against the members as a whole.
"We don't hold reserves year to year so any action that any one individual club takes effectively the burden of that would fall on all the other members."