Finding a way to hold harmless up to 5,000 teachers who have maxed out on their pay raises for education and seniority may be the key to averting Chicago’s second teachers strike in four years.

Days after the Chicago Teachers Union’s 40-person bargaining unit pushed for an October deadline, sources with knowledge of the negotiations outlined a possible pathway toward an agreement.

The $5.4 billion budget approved this week by Mayor Rahm Emanuel’s handpicked Board of Education includes a $250 million property tax increase for teacher pensions and assumes $31 million in labor concessions reached partly by phasing out a 7 percent pension payment awarded to teachers years ago in lieu of a pay raise.

Sources close to the negotiations described eliminating that “pension pickup” as a non-negotiable “structural reform.”

But instead of phasing out the 7 percent CPS contribution over a two-year period, sources said it’s possible teachers could be asked to assume the burden over a three-year period.

Even more important are the 4,000 to 5,000 teachers who have been on the job for 14 years or more and are in the highest of the “steps” for experience. Unlike lower steps that see an increase for experience every year, steps 14 and 15 require upward of five years’ service each before maxing out on step 16 in their 25th year.

That pool of veteran teachers would still come out ahead at the end of the four-year contract because of annual pay raises that would leave the average teacher with 6 percent more, even after phasing out the pension pickup.

But the veteran teachers in the top three steps would come up short in the second and third years of the agreement so far.

Holding them harmless would cost roughly $8 million. Finding the money to do just that could hold the key to an agreement, and it’s likely to be a focal point for ongoing negotiations.

CTU attorney Robert Bloch agreed that “not everybody gets a step” and that the union takes issue with treating those steps as annual increases but rather “as something reflecting your longevity and learning your craft.”

“If the contract is valued as steps as being part of the compensation, those teachers are left out,” he said. “The step should not be counted, they should look at across the board raises. That’s an area of disagreement between us.”

Bloch continued, “The union’s position is no cuts. So they are not agreeable that any teacher takes home less pay. The school board’s books should not be balanced by taking money out of the paychecks of teachers,” nearly all of whom live in the city and are paying higher property taxes imposed by City Council and the Board of Ed.

“The deal that we reached on Jan. 29 is a fair foundation for a final agreement, and we are open and willing to listen to any ideas that the CTU leadership presents to make the framework work better for both parties,” district spokeswoman Emily Bittner said. “CPS’ continued objective is to give teachers a raise that works within our budget constraints, especially since we just passed a tight budget that included significant tax hikes on Chicago homeowners, Central Office staffing reductions and revenue from Springfield.”

She also highlighted several quality-of-life elements, reached in last winter’s agreement, that the CTU has long requested, such as reduced paperwork, grading autonomy, evaluation changes and more community schools.

Several sources said Emanuel, schools CEO Forrest Claypool and the teachers union still agree to “go together to Springfield” to push for a graduated state income tax that could provide a windfall for CPS.

As it is, the CPS budget is precariously balanced on the assumption of $215 million in pension help from Springfield that’s contingent on a solution to the state’s pension crisis. That’s a huge “if” considering the marathon budget stalemate between Republican Gov. Bruce Rauner and Democratic legislative leaders who control the Illinois General Assembly.

Earlier this year, a much-anticipated report from an independent fact-finder tasked with sorting out the teacher contract dispute was “virtually unchanged” from an offer the union shot down in February.

That put CTU President Karen Lewis in a box to try to re-sell the deal she was unable to sell before to her union’s more radical elements, or consider leading her members out on strike for the second time in four years.

The proposal that Lewis had labeled a “serious offer” included net raises over four years; the phasing out over two years of a 7 percent pension contribution CPS has been making on members’ behalf; and a return to raises for continuing education and experience as soon as the next school year.

None of those main economic points changed in the findings made by independent arbitrator Steven Bierig. Neither did the improved teaching conditions offered in January. Those include giving teachers more power over grading, increasing the number of community schools and eliminating burdensome paperwork — all improvements the CTU has demanded.

The union’s “Big Bargaining Team” unanimously rejected the offer, saying CPS needed new revenue or it was offering raises while requiring a set number of teachers to retire. It also didn’t count on CPS to be able to enforce a cap on charters while a state board still has power to overturn the district’s decisions.

Even if a way can be found to hold harmless the 5,000 most senior teachers, sources said Lewis will have to play a more active role in “selling” the new contract. It won’t be enough to simply call the deal a “serious offer” and let the chips fall where they may.

Ald. Pat O’Connor (40th), the former longtime chairman of the City Council’s Education Committee now serving as Emanuel’s floor leader, was somewhat pessimistic when asked whether he believes Chicago can avoid a bitter repeat of the 2012 teachers strike.

“The teachers seem to be drawing a real line in the sand. If they stick to the idea that they’re not gonna pay one more dime toward their pensions and they want a salary increase, it’s almost inevitable” that there will be a strike, O’Connor said Thursday.

“If those are the requirements not to strike, I don’t think we can meet those requirements. There’s no money,” he said. “The budget itself is balanced on the good will of Springfield. It’s a very precarious thing to begin with. The additional money we acquired from Springfield was predicated on us getting help from the other quarters [including teachers]. And it’s not enough to accomplish the goals that teachers have set out. But if it’s a bargaining, hopefully we’ll get to a place where we can all agree.”