This won't be the most thorough answer, because this isn't really my field, but your question reminds me of an article by Ainslie Embree contrasting modern and pre-modern states, so here goes:

Most ancient empires lacked a clearly defined border at the edge of their territory. Their power was limited to the areas which they could tax, extract manpower and natural resources, etc., and some regions were simply too far removed from the center to allow constant control. The ambiguous nature of these borderlands meant it was fairly easy for claims of different polities to overlap, thus allowing further expansion when one power felt it had the upper hand in the region. Empires are expansionist by their very nature, and the lack of any clearly defined borders or strong sense of nationality meant that it was extremely difficult for any neighboring states to co-exist entirely peacefully in the pre-modern era.

The Holy Roman Empire and Byzantine Empire coexisted for several hundred years fairly peacefully. They were very competitive and Byzantium rulers were not happy with the Pope's crowning of an Emperor in the West (Holy Roman Emperor) but these were cultural and religious differences that didn't tend to lead to wars. A major reason for the Pope launching the first crusade was to relieve pressure from the Byzantines who had been losing territory to Muslim forces for centuries. There were issues too, as the Greek and Italian/Germans did not get along, and the Byzantines worked with Muslims later against Crusaders. But for the most part, the 2 empires co-existed as well as empires can. Lost to the West by Lars Brownworth is a great introduction book to the Byzantine Empire.

Also I would say the empires of Spain and Portugal co-existed relatively peacefully though I am not as familiar with them as the HRE and Byzantine Empire.