I suspect that the best case for the arabs would be for the Syrians to be that little more threatening in the north (maybe Lebanon or Jordan threaten to join the party). Israel basically throws its reserves north at the Syrians, and beats them back past the golan. They win a decisive victory in the north, but are faced witht he prospect of Egyptians almost regaining the Siani. Then Israel is faced with the prospect of a negotiated ceasefire (possible, but does Meir know that?) which probably involves giving back the Siani or a prolonged war as they try to drive the Egyptians out (Egypt was not particularly good, but they were better than the Syrians; Israel might beat them, but it would be tough, and they cannot afford the war to drag on to long).
Of course, if Israel goes with the nuclear option at some point, obviously the aftermath will be somewhat different.
Egyptian army crossed the Suez, repelled the initial (and expected) Israeli counter attack then dug in and waited under SAM umbrella. When Syrians were getting mauled in the north Egyptians, after much Syrain proding, moved out, which was a disaster for them.
Until that time Egypt achieved their military goals, except for heliborne assault on Mitla and Klidi(?) pass which was not such a disaster after all.
After IDF initially threw their strength at Egyptians they realised that Syrians were far more dangerous, due to simple fact that Syrian breakthrough would
allow them to threaten Israel proper while Egyptian breakthrough/advance would only get them into Sinai, which was a good buffer.
Egyptian actions, most notably the digging in and waiting, also showed Israelis that Egypt had limited objectives so they knew that Egyptians could be left alone while Syrians could not.