The first meeting of the SPFL's Reconstruction Group on Monday has been described as "positive and constructive".
The remaining 14 members - cut by one after Hibs chief executive Leeann Dempster pulled out - came together via video conference on Monday, just a few days after it had been formed.
It is being co-chaired by Hearts owner Ann Budge and Hamilton chairman Les Gray, who were the only two Premiership voices, with four Championship clubs, three each from League One and Two and one representative from the Lowland and Highland League also involved.
The group will reconvene on Friday to discuss next steps, with the Premiership currently suspended until at least June 10 and all other football having been cancelled.
There will also be 15 people at Friday's get together with St Mirren chairman Gordon Scott having joined as the third Premiership member with a club statement saying they "wanted an input into the talks taking place" and "would be interested to hear all positive ideas on this matter."
Gray said: "The first meeting was positive and constructive with a wide range of thoughts being shared across the group. It's important that we now use the next few days to consider these initial discussions very carefully.
"We will reconvene on Friday with a view to developing a more focused approach that we can take forward into what I hope will be meaningful progress."
Budge added: "The meeting on Monday was very enlightening and it was really interesting to hear comments from across the divisions. There was a broad range of opinions shared so it will be important that we find common ground moving forward.
"It was clear to me that there is an understanding that we are facing a totally unprecedented situation but I do believe the desire for change is still there."
Dundee United will be promoted to the Premiership, Raith Rovers move up to the Championship and Cove Rangers' rise through the ranks continues after they were crowned League Two champions and promoted.
Partick Thistle will be relegated from the Championship and Stranraer drop into League Two, while no decisions have yet been made on Lowland League winners Kelty Hearts and Highland League champions Brora Rangers.
Hearts face relegation from the top division if the Premiership is unable to restart, but more clarity on that is expected on Thursday when UEFA's Executive Committee is expected to announce new guidelines on associations being given the go-ahead to end the 2019-20 season early.
One proposal has already been made by Premiership club Livingston, which would include a 14-team top flight, saving Hearts, and both Kelty Hearts and Brora Rangers being brought into an expanded 44-team SPFL structure.