NGO Superpower: Actually, yes. Quite a lot, especially given the sheer range of government sizes out there, and the sizes therefore of the organizations that some of the real behemoths can host.
For a start and most prominently, most of the “Big 26” starcorporations at least have the financial resources to stand in the same rank as many large governments (and often have extensive conlegial and/or extraterritorial holdings), and above the small ones. Special note here goes to Gilea & Company, ICC, the banking starcorp which routinely makes large sovereign loans out of its private assets and treats polities no differently from any other customers – and when Gilea & Co., who stand behind or advise, in one way or another, an appallingly large percentage of the galactic economy, sneezes, entire economies catch the plague and die;
Ring Dynamics, ICC, which owns and leases most of the galaxy’s interstellar transportation network;
And Ultimate Argument Risk Control, ICC, which provides security services, military contracting, and mercenary brokerage, and if it cared to gather all of the forces beholden to it in one place, could make a respectable showing against most Great Power fleets, and unquestionably defeat lesser polities on its own. (It doesn’t; its owners aren’t interested in assuming the responsibilities of sovereignty, and agree with the unspoken “Iron Concord” among the Powers that mercenaries should be paid to make war, not paid not to make war. But it is happy to rent its mercenaries to other starcorps in need of a forceful solution to Static defaulters or expropriators, pour décourager les autres.)
(While no individual runs it or controls it to any significant extent, the collective intelligence of the Seranth Exchange has similar potency when it comes to the way that shifts in its market can affect things out and about in the Worlds.)
The others are less obviously potent, but smart polities understand that it’s a bad idea to make an enemy of say, StellEx (if you want your logistics to keep moving), Bright Shadow (who sold you your Internet), Telememe (who publish the news that the newscorps read), Traders in Ideation (unless you love getting FRM errors), Riverside Eubiosis and Crystal Flame (since your citizens may not appreciate a renewed outbreak of mortality), etc., etc. Even much smaller starcorps than the 26 are accustomed to negotiating terms with local governments on a much more even footing than one might expect.
There are also, of course, a number of “non-politan”, unaligned seed AIs, who despite being singleton intelligences have all the production capacity and coordination ability of a (usually minor) polity.
A number of non-profit groups, mostly a mix of “direct action charities” and more self-interested “information brokers” – some of both of which are functionally privately run intelligence agencies – are in approximately the same league as some of the smaller starcorps – they have to walk a bit cautiously around (which by no means means “avoiding conflict with”) the Powers and the larger polities, but on those occasions when they think it will help – which, in fairness, they usually don’t, because it rarely does – they can slap a few smaller polities and single-system nations around a bit. And a lot of them are more than happy to hire UARC or other merc outfits for this purpose, when necessary, although the latter especially prefer manipulation and memetic subversion than getting into out-and-out conflict.
And out in the Expansion Regions and other more shadowy corners of the worlds, some less scrupulous large mercenary organizations and the odd criminal syndicate can exert a lot of influence over local politics, more than enough to hold their own against the local polities.
Oddly enough, averted where most terrorist organizations are concerned. Mostly because unlike most of the above, by definition the terrorist organizations go too far – which is unfortunate for them when the opposition tends to be people like the Imperial Navy, whose Combat Pragmatism and notions of cost-effectiveness are such that, for example, if told that the terrorist leader is hiding in an impenetrable range of cave-ridden mountains, will reply “okay, fine, we’ll just bombard them from orbit until the sonofabitch has to learn to breathe lava”. And if it’s something less terrain-y – well, the Laws and Customs of War are very clear on this: voluntarily standing in the crowd the enemy is hiding in, once you’ve been warned, is giving aid and comfort to the enemy and the ensuing predictable consequences are entirely your own fault.
Subverted a little with the Conclave of Galactic Polities, even with the tremendous law enforcement powers and independence of the Operatives of its Presidium, mostly because it works very much for the highly select list of Great Powers making up said Presidium.