To make this work you need either one of two things to happen
1. Better coordination between Persians and Byz would have not allowed significant reinforcements reaching the Muslim forces at Yarmuk most likely leading to a Byz victory in day 1 or 2.
2. This would not have allowed for the 6000 + Muslim elite troops marching back to fight the Persians at the Battle of Al-Qadisiyyah leaving the Persians most likely victorious.
3. After this you would have seen a concerted effort that would have allowed the Byz / Persians to hold the borders and regain their normal strength
a. Since Khalid left Iraq for Syria, Suwad, the fertile area between the Euphrates and the Tigris, remained unstable. Sometimes it was occupied by the Persians and sometimes by the Muslims. This "tit-for-tat" struggle continued until emperor Yazdgerd III consolidated his power and sought alliance with Heraclius in 635 in an effort to prepare for a massive counterattack. Heraclius married his daughter to Yazdegerd III, in accordance with Roman tradition to seal an alliance. Heraclius then prepared for a major offense in the Levant. Meanwhile, Yazdegerd ordered a concentration of massive armies to pull back from Iraq for good. This was supposed to be a well coordinated attack by both emperors to annihilate the power of their common enemy, Caliph Umar.
b. When Heraclius launched his offense in May 636, Yazdegerd could not coordinate, so the plan was not carried out. Umar, allegedly having intelligence of this alliance, devised his own plan. He wanted to finish off business with the Byzantines first and then to reinforce the Muslim army at Yarmouk. He sent 6000 soldiers in small bands to give the impression of a continuous stream of reinforcements. Meanwhile, Umar engaged Yazdegerd III, ordering Saad ibn Abi Waqqas to enter in peace negotiations with him by inviting him to convert to Islam.[18] Heraclius had instructed his general Vahan not to engage in battle with Muslims until his orders. However, fearing more reinforcement for the Muslims from Madinah and their growing strength, the Byzantines felt compelled to attack the Muslim forces before they got stronger. Heraclius's imperial army was annihilated at Battle of Yarmouk in August 636, three months before Qadisiyyah, ending the power of the Roman Emperor. Nevertheless, Yazdegerd continued to execute his ambitious offensive plan and concentrated armies near his capital Ctesiphon. A large force was put under the control of veteran general Rostam and was cantoned at Valashabad near Ctesiphon. Receiving news of the preparations of this massive counter-attack, Umar ordered Muthana to retreat to the edge of Arabian Desert and abandon Iraq. The campaign of Iraq was now to be started again from the beginning.[16]
c. Caliph Umar raised new armies from all over Arabia to send a large enough force to re-invade Iraq. Umar appointed Sa`d ibn Abī Waqqās, an important member of the Qurayshtribe as commander of this army. In May 636, Saad marched from his camp at Sisra (near Madinah) with an army of 4,000 men and was instructed to join other armies, concentrated in northern Arabia, on his way to Iraq. Saad, being less experienced in the matter of war, was instructed by Caliph Umar to seek the advice of the experienced commanders. Once Saad entered Iraq, Umar sent orders to him to halt at al-Qadisiyyah, a small town 30 miles from Kufah. Muslims marched to Qadisiyyah and camped there on July 636.
d. Umar continued to issue strategic orders and commands to his army throughout the campaign. He wanted victory on the Persian front, but he ran short of manpower and decided to lift the ban on the ex-apostate tribes of Arabia from participating in state affairs. As a result, the army raised was not professional but was instead composed of newly recruited contingents from all over Arabia. Umar was therefore more concerned about providing it with strategic aid. Umar was quite satisfied with developments on Byzantine front, however, as the veteran army there was commanded by Abu Ubaidah ibn al-Jarrah and Khalid ibn Walid, a military genius. After they won a decisive victory against the Byzantine army at the Yarmouk, Umar sent orders to Abu Ubaidah to immediately send a contingent of veterans to Iraq. Later, a force of 5,000 veterans of Yarmouk were also sent and arrived on the second day of the battle. This proved to be the turning point. The battle was fought predominantly between Umar and Rostam, rather than between Saad and Rostam. On the other hand, the bulk of the Sassanid army was also made up of new recruits since the bulk of regular Sassanid forces was destroyed during the Battle of Walajaand the Ullais.[16]