Could the Rus' Khaganate, later Kievan Rus' federation, or the Republic of Novgorod have taken on heavy Norse influence, possibly eventually seeing itself as an extension of the Scandinavian kingdoms? What events could have transpired to expand the areas of Varangian settlement in Kievan Rus'?
To start off the discussion, here are some possible PODs.
1. Incomplete conquest of Kiev, more northerly Rus'. What if the Varangians never reliably took control of Kiev? It's possible that the Varangians might never subjugate the city in the first place, leaving it as a settlement of Slavic/Iranic tribes or as a Khazar trading fortress. Alternatively, the Varangians might initially subjugate or take control over the authorities of Kiev, but then, the Khazars (potentially with Byzantine, Bulghar, or Abbasid backing) manage to raid Kiev one or more times after its acquisition, destabilizing the city, and decreasing the city's influence while severing its connection to the other East Slavic regions of the then non-Kievan, but still Varangian Rus'.
I would argue that this would decrease the area of land settled by the Varangians, without significantly decreasing the number of Varangians settling the region. On one hand, while less loot would be taken by Norse adventurers on Viking expeditions, at the same time, there would be a higher need for Varangian mercenaries to guard the less secure frontier, leading to more invitations of said mercenaries from Scandinavia. Loot, in any case, did not constitute as much of the Norse wealth in the East as one might initially expect based on their actions in the west. For example, the Norse expeditions to the Caspian Sea, if reading only the written historical record, were all failed enterprises. Instead it was by and large, the non-military expeditions of trade with the Khazar and Islamic realms which, as shown by the archaeological record, brought goods and Islamic silver through the Rus' lands and into Scandinavia. A prosperous Khazar Khaganate increases trade so much that even more extensive control by the Khazar Khagan at the expense of the Rus' may not mitigate the actual settlement of the Rus'.
Restrict the same amount of Varangian influence into a smaller area, and they may end up forming a permanent base to expand from. They could form a "Republic of Novgorod"-esque state earlier, which becomes the center instead of Kiev.
2. Khazar Khaganate survives, Pax Khazarica maintained. The archaeological record shows that the flow of Islamic silver into Scandinavia declines significantly in the 950s, in a trend that continues into the 970s. There have been a number of proposals as to the causes, focusing on all sorts of factors. I believe it was probably an effect of the long-term decay in the northern Eurasian trade routes. Particularly, this exacerbated by the sharp decline of the Khazar Khaganate and the gradual decline of the Abbasids in the period. It was in the 960s that the Khazars were essentially destroyed as a state with any real influence, by the expeditions of Sviatoslav I of Kiev. Since the Khazars kept peace and vitalized trade routes over a large area that would later become quite unstable after their collapse, it's seems like no coincidence that the Varangian influence, and indeed the Viking Age starts to decline after the Khazars do. If we keep the Khazars alive, either by having the expeditions of Sviatoslav fail, or the Norsemen make an alliance with the Khaganate, then the emporia system survives longer, potentially allowing for a continuation of Rus' connections with the Norse at least in terms of continued invitations of Varangians.
3. Abbasids retain Mesopotamia, strengthening Islamic trade routes. Another event that occurs in the mid 10th century is the terminal decline of the Abbasid Caliphate, when the Buyids seize Iraq and the Abbasid state loses all real authority over the region. I don't know much about the effects of the Buyids on trade, but it seems like the decrease in trade between northern Europe and the Islamic world in the final centuries of the Early Middle Ages, could certainly be connected to the military conflict that devastated the Abbasids. As such, it seems reasonable that to increase the vitality of Islamic trade routes, one could preserve the Abbasid power. Indirectly, this could prolong the economic viability of Norse trading settlements in Kievan Rus' who played a role in connecting these areas with Northwestern Europe.
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What do you think about each of these PODs? Do any of them seem feasible for creating a more "Viking" Rus, or is the historically Byzantine influence in medieval Russia too powerful to overcome?