St Mirren chairman Gordon Scott has been added to the SPFL's reconstruction group, the club has confirmed.
It comes a day after Hibernian chief executive Leeann Dempster withdrew from the 15-person panel to focus on identifying "how and when football fans can safely return to Scottish grounds".
The group met for the first time on Monday and will reconvene on Friday.
"The first meeting was positive and constructive," said Les Gray of Hamilton Academical.
Fellow co-chair, Ann Budge of Hearts, added: "There was a broad range of opinions shared so it will be important that we find common ground moving forward."
Any proposal to reconfigure the leagues will go to a ballot of the SPFL's 42 clubs.
The taskforce was set up in the wake of a resolution being passed to end the lower leagues. Hearts face being relegated if the Premiership is also curtailed and no reconstruction takes place.