I can see a few ways
1) Under earlier Emperors - push the Arabs to unite under the Lahkmids, against the Persians - not easily done, but I don't see it as impossible. Cheaper than going to war against the Persians directly, alternatively the Tanukids - instead of being alienated, instead pushed to work with the Ghassanids. TL;DR - Create a strong, Pro-Roman Arabia, rather than a powerful hostile one.
2) Under Justinian - ensure that you have other good generals, and resources for fighting Khosrou. Ideally don't build the Hagia Sofia until Italy is reconquered. Instead, spend that money on giving Belisarius the resources he needs to (perversely honourably expect for one trick) conquer Italy. The first time around - this would maintain much of its wealth, circumvent the Gothic Wars, and provide the later funding for the Hagia Sofia in the later years of Justinians reign. Whilst the Plague will still hit, with resources better allocated to a rock-hard defense against Khosrou, the Plague will be less catastrophic, as the Empire hasn't been stuck at war - and both Rome and Persia can weather the storm. This should allow Africa to easily be expanded, and perhaps southern Spain. TL;DR - More militarily generous Justinian - more troops, faster conquests, faster assimilation, rather than bogging Belisarius down in Italy forever.
3) Komnenos - Manuel specifically, circumvent the wasted resources invading Egypt, and instead encircle the temporarily pacified Seljuks of Rum, and secure eastern Anatolia, rather than suffer war with them. Encirclement would ensure that they could be completely dealt with later. Sure the Crusader states suffer, but they can be reconquered later.
4) Eastern Alliance with the White Huns. Agreeing to give the Iranian Plateau to the White Huns, whilst keeping Anatolia crushes the Easts major rival, whilst saddling their new neighbour with a large restive population. This would give the East time to recover, and take over Arabia, securing the East in Mesopotamia, allowing free reign in the West.