Hegemony isn't union. Leadership isn't ownership. Given those assumptions, we are geographically constrained.
Maximizing pure area requires as a starting condition that some huge, easily held region of the world is included. Probably, we're talking about either the west-Urals and Siberia, or Canada and Alaska. There's also Antarctica, Australia, and the Sahara, but.... The first manages to be both too worthless to occupy properly and too accessible to be easily claimed by a single power. The Sahara is much the same, but less easy and with the added feature of isolation from geographically large powers and potential powers. The latter is also true of Australia which, while otherwise ideal for our purposes, is heinously difficult to federate with anything more substantial than New Zealand.
Which brings up the other major factor: a superpower. A prerequisite is a huge, contiguous, and culturally uniform(-ish) area with enough water, agriculture, and resources to allow a state centered on it to easily project into both the easy spots mentioned above and a few more difficult ones. That requirement limits us to India, China, European Russia, west-central Europe, and that-place-where-America-is.
The trouble is getting both items adjacent. The first two, despite looking decent on a map, actually have enormous geographic, cultural, and economic obstacles to expansion beyond their core areas. Siberia is well blocked off from China, though they could do passably better in Central Asia, but India's pretty much stuck. West-central Europe is actually very small, relatively speaking, and what would they annex, anyway? And why? In essence, then, we're limited (doing it the easy way) to the *US and Russia.
China also had the potential, but getting it to commit to Central Asia again, and bother with North Asia, is a lot less simple than straight wanking the above two. Nor would I rule out British-based imperial federation entirely. But you have to do a lot of justification work and background to even get them started. And anyway, with Rule Britannia you can get India and Africa or you can get the Dominions, not both.