I was thinking something where the first part of the war has both sides dealing heavy damage to the other, so neither side can win but both can hurt the other badly. Then they both go to the diplomatic table.
Normally I would agree with this, but with the Emancipation Proclamation freeing the South's slaves, I don't think a compromise could possibly be reached. The Proclamation wouldn't (and really couldn't) be rescinded, and if the South loses slavery, then it's lost the war.
Actually OTL the two sides did meet at the diplomatic table late in the war, in 1865; Lincoln (who met with the Confederate representatives in person) offered that the seceded states could be immediately accepted back into the Union, to delay the passage of the 13th amendment by a few years, and indicated that he could get enough wealthy backers to pay for the South's slaves, in exchange for the South re-joining the union. Apparently some Confederate advisers wanted to take up the offer, but Jefferson Davis shot it down.