One of the ways I dealt with it IMTU was to treat the Solomani Party (and Confederation) analogously to the medieval Catholic Church and Western Christendom.

The Confederation had no _direct_ power over the various members of the Confederation (who often squabbled between themselves), but it definitely had a role co-ordinating the Solomani polity, if only by "excommunicating" Confederation members who strayed too far from the Party line (thus making those "heretic" states vulnerable to power plays from internal opposition factions, and external rivals keen to take advantage).

From an adventuring POV, it also created a nice dynamic where local politicians could be like medieval bishops: part of the local power structure, but also representatives of the broader Party.  Where do the real allegiances lie?

This also explains how the Confederation remained intact after the loss of 1/3 of their worlds, 1/2 of their population, and Terra itself.  The lost member states were gone.  The remaining member states were no weaker (having lost no worlds), and still had Solomani Party membership at the very heart of their governmental structure.  The loss of Africa, Sicily, and Spain to Islam did not make the Papacy non-viable and, if anything, provided consolidation opportunities to nations like Francia.