According to Touring the Stars, the Rim Collection and Rim Territories have benefited from Lyran ex-patriots colonising nearby in an effort to escape the Jihad, as well as, strangely, some worlds wanting to break away from the Lyran Commonwealth.
I was also reading Field Manual: Periphery, and it seems after the Rim Territories attacked the Rim Collection, they were beaten back and followed, losing one of their two worlds to the Collection. Presumably they took it back at some point, but it mentions some pretty strong anti-Collection feelings on the part of Morrison. Yet, by 3130, he’s probably long gone.