Apparently what the Big Three decided this evening is that the new president should be a woman. Which... actually narrows things quite a bit, barring an upset. Casellati was initially the strongest candidate as far as women went, but then Salvini tried to force her through, and the failure of that attempt leaves her candidacy dead in the water. That leaves Elisabetta Belloni, a prominent career civil servant with a focus on diplomacy and intelligence agencies. She's apparently well-liked across the board, so she makes a ton of sense as a compromise candidate. But it ain't done till it's done.
I do wonder where all these Mattarella votes are coming from now...