His body and the spl will set up "a working party" to further assess plans discussed by the SFA's Professional Game Board yesterday.
The SPL wants two leagues of 12 and made their first pitch to attract clubs from the SFL at the Hampden summit. Longmuir said: "I feel that we've established a lot of common ground between all parties and that's what we're going to take forward and build on.
"The next step will be to build on the common ground and meet again later this month, hopefully, and further develop the areas of common ground, which there was a lot of.
"I'm satisfied as head of the SFL, it was a very constructive, positive meeting. Everybody came to the table with a willingness to improve the game and do our best for the game. I was greatly encouraged by it. You'd be amazed by the common ground we discovered amongst all of us."
SPL clubs had last month unanimously backed an idea for two top leagues of 12 which split into three divisions of eight after 22 games, with an 18-team bottom league.
SFL clubs had just days before set out vastly different plans for a 16-10-16 structure.
But the SPL are hoping to persuade their SFL colleagues, with the promise of wealth redistribution and more movement between the divisions.
The working party will consist of representatives of six SPL clubs: Celtic, Hearts, Aberdeen, Kilmarnock, Dundee and St Johnstone, with representation from the SFL yet to be nominated.
SPL chief executive Neil Doncaster, Longmuir and two as-yet unnamed SFA representatives, likely to be chief executive Stewart Regan and president Campbell Ogilvie, will also be in the group.
SPL plans for reconstruction would involve asking the SFL to disband and merge with them to create a new governing body or invite applications from the SFL clubs, with applicants' league position the key factor.
The proposals would relax criteria for SPL entry, including its ban on artificial surfaces.
Longmuir added: "Don't get hung up on the plans – it's the principles that we all found loads of the common ground on. So we've got to work on that and further develop it.
"I'm not too worried about the plans in terms of the numbers. The common ground and the areas where we all felt exactly the same way about the game and how we take it forward, that was the real encouraging thing.
"There was a lot more to this than just the plans. It was about common ground, it was about the principles, it was about doing the right thing for the game, it was about they key things that matter to the game going forward. I think that's what we achieved."
A statement from the SFA's Professional Game Board said: "The first meeting of the working group will take place later this month and will also include representatives of the Scottish FA Board.
"The PGB are greatly encouraged by the willingness on both sides to engage on the many areas of common ground and also in their commitment to implementing change.
"After the working party have reached consensus on a final set of proposals, they will be presented to all clubs across the SPL and SFL for consideration."