By doing so the leadership of the party hopes to avoid an embarrassing defeat on a marquee issue at the party conference currently being held in Gothenburg.
The party leadership has previously said that it does not want to ban companies in these sectors from taking out profits outright, but there is broad opposition within the party to profit taking in these sectors.
Negotiations were underway all day Thursday, and late last night the party leadership proposed a more strongly worded policy statement in the so-called "Contract for the Future", a document which contains the party's policies were it to win the general election in 2014.
The clearest change the party leadership is proposing comes within the area of privately run schools.
They wrote: "Municipalities should have the possibility to actively plan when and where new schools should be opened to counteract the growing problem of school segregation and to ensure that children and teenagers with different backgrounds and circumstances are given the same chances. Newly established schools that lead to segregation should not be allowed to open and municipalities should have a deciding influence over their establishment."
In essence, the proposal would give municipalities the power to veto, to say no to a new school that wants to establish itself - a power municipalities do not have today.
The statement goes further than earlier formulations. In their first proposal, the party leadership said only that the schools should have "more influence" over the opening of new schools.
The question now is whether the opponents in the party will accept the compromise.
Swedish Radio news reports that members from Skåne county, among others, have called for a more far-reaching statement. "Considering that it's a new proposal, I'm expecting it to be a sharper statement towards a non-profit policy," said Joakim Sandell, a Social Democrat and leader of the Skåne delegation.
Party members are expected to hold a vote on the wording late in the day on Friday.