Despite nominal civilian control over the Starfleet (which was founded as a paramilitary organization but has since been absorbed as the only effective military force in the GRA), the Starfleet maintains a fierce independence from direct bureaucratic control, with their own internal procurement and administrative structure outside of the Advisories, including the Military Affairs Advisory that serves as their Oversight. The Starfleet is commanded by the Sky Marshall, who is perhaps the second-most powerful officer in Alexzonyan government and answers, in practice, only to the President. While the power to declare war formally lies with the Senate, in practice the official declaration is window dressing, and the President and Starfleet have full freedom-of-action in lieu of direct intervention of the Senate (which, to date, has never occurred).
While lower jurisdictional governments (planetary, regional, municipal) exist, these secondary and tertiary governmental organizations are strictly subordinate to the national government and exist only because of the administrative issues that arise from attempting to centrally run an entire nation of 16 inhabited worlds with a single massive bureaucratic monolith. Instead, the various levels of bureaucracy work together to form multiple smaller bureaucratic monoliths contained within the shell of the largest.
While xenophilic and accepting of outsiders, one safeguard included in Alexzonyan governance is a so-called “Heinlein Law”; national service is required as a precondition to citizenship, even for native-born Alexzonyans. This ensures that most members of the Alexzonyan electorate are committed to the success of the Alexzonyan state and, coincidentally, requires any new inhabitants that might have cultural values in conflict with Alexzonyan norms to serve in the government for several years, giving Alexzonyan values a chance to win over new converts and the newcomers a chance to socialize to Alexzonyan norms prior to gaining full citizenship.
Politically, the Senate is elected proportionally and the President, while elected nationally by popular vote, is determined by a preference-ranking ballot system. This allows more than two parties to credibly exist, and a number of minor parties have come and gone over the years. At present, four major parties with national presence exist: The Alexzonyan National Party, the Conservative Party, the Liberal Democrats, and the Progress! Party (being far-right, center-right, center-left, and far-left, respectively). Of course, these positions are relative to the existing politics of the GRA, which are well to the left of the galactic mean; the Conservatives would be left-leaning in most other NS polities, and the abhorred-in-many-circles “far-right” Alexzonyan National Party bears resemblance to the post-2016 Republican Party in the United States. Minor parties with no noteworthy national presence but with formal charters include the Altreshi Independence Party (basically dead, but still formally chartered), the Libertarian Party (they like the Dornalian flag), the Transcendence Party (they like the Phoenix Domain flag), and the Alexzonyan Communist Party (they’d like a flag, but I’m told Communist has never been tried).