Given the small size of most of the empires, you mentioned four worlds / 1 trillion, I may go up to 100 worlds with a similar population limitation, there will be a number of extra-governmental organizations. You mentioned two: the Galactic Assembly and the Courier service. There will undoubtedly be others.
I am sure there could be empires with a 100 or 1000 comparatively sparsely settled worlds, but eventually, they would break apart when their population grows. Also, spreading one's population is, at first, less efficient than concentrated pockets of settlement. Only growth justifies such a spread, and with eventual splitting of widespread empires being a given, the will to colonize will have limits.
One immediate idea is mega-corprations. These large corporate entities serve markets across several empires, and broad swaths of space. I would think that if governments can't manage to keep a group larger that 1 trillion together, most of the corporations would limited to a similar size.
Likely much smaller, because they lack the tools that a government has at their disposal. No laws, no patriotism, no greater good, no (signifcant) armed forces. Most don't even have a genuine mission besides "want to earn a living, and then some", and even those few that do cannot possibly expect most of their employees to burn for that. I'd expect the largest private organizations to have no more than a billion members or so, and even that seems optimistic to me.
Also, many governments will simply protect their own companies at the expense of foreign-based ones, I believe. With no "great powers" that could dominate the entire galaxy or even a significant fraction of the local theatre, "globalization" is a lot harder to do.