Your challenge is to have Sogdia be considerably more successful than it was IOTL.
Well first things first, you'll have to prevent the rise of an Islamic Persian identity, because that was ultimately the downfall of the Sogdians - rapid assimilation at the elite level to Persian culture in the centuries following the arrival of Islam. Their language was on the way out by the twelfth century, iirc.
So you have a relatively narrow historical window with which to make Sogdia influence the world. The region was largely depopulated and based on subsistence agriculture until about the sixth century, when migrations and urbanization began again in earnest. But Sogdia never was a united and independent polity. There were almost always stronger local powers who controlled her cities. And being a settled people living in a region largely controlled by nomads, they have significant disadvantages when it comes to creating a Central Asian empire.
I'd suggest that one of the best ways to make Sogdia more influential would be to lengthen and enhance the era of Turkic dominance - a sort of "Turkish peace" across all of Central Asia all the way to Manchuria. Into this void step Sogdian merchants, spreading their culture and language and establishing colonies and little Sogdian quarters as they go. There's definitely room for a greater expansion in this manner - Sogdians played a huge role in OTL's silk road and if things could somehow remain stable for a long time maybe you could get them to have an enduring role as middlemen and colonists across Central Asia. Then you just have to ensure no Iranic dynasty with sufficient cultural prestige to enforce the assimilation of their ruling elite comes along...
Aah. One of my favorite subjects!
It looks like the Sogdians weren't some kind of homogeneous ethnicity. They were Semi-Nomadic people living in Tajikistan, Uzbekistan, Afghanistan and Tarim Basin. They were multi religious. They had extensive interactions with the surrounding Tocharians, Scythio-Khotanese, Bactrians and the Bactrian Greeks, along with interactions with the Persians, who were a bit distant.
I am unsure how you could get Sogdian wank without getting them into a confederation like the Yuezhi and the Kushans(the subclan of the Yuezhi).
The land they lived around wasn't very hospitable to support large and populous empires. To cross over into greener regions around the Volga will need the confederation to confront the Nomadic Scythian warriors and find a way to assimilate the Volga Finns and the other Volga Uralic people. However, we could have a confederation of Sogdians, their close friends, the Tocharians and other Eastern Indo-Iranian people like the Wusun plus any willing Scythian(Iskuzai) clans or "Zai". They could create an Empire encompassing the Tarim Basin, lush and fertile Issyk Kul region, Sogdia, Transoxania, Bactria and then venture into the Volga-Ural region after strengthening. Could this work out?
Another way is to create a Second Kushan Empire, this time with a larger confederation, which would contain Sogdians, Tocharians, Scythians and probably even the Wusun(they were probably there even with the Yuezhi Kushan clan of the first empire). This would have their populations in Peshawar region(capital of the Kushans), Bactria, Helmand, Gandhara, parts of Iran and the Punjab region. The latter empire maintaining a Sogdian population as it is, would be unlikely as the region is already populated.
The former Confederation that could create an Empire on the Ural and Volga could create Sogdians as an ethnicity like the Germans, who are diverse in origin but are a single ethnicity today.
Sogdia finds itself in a difficult position, perhaps a geopolitical nightmare. As said, from the west, you need to preserve your identity from being swallowed by the Persians, from the north you need to prevent the Turkic peoples from overwhelming you.
I mean Sogdia is synonymous with Uzbekistan, partly Tajikistan. Uzbekistan today is a Turkic nation .
Problem is that there is no natural barrier to the north that would be easily defensible