Basically, the campaign is going to be XCOM: Enemy Within with Eldritch Characteristics. The base story is straightforward: aliens invading, humanity needs to fight them off. Here is a link to the basic XCOM: EW campaign for reference.
Where I want it to get interesting is with the various different factions (which need lore.) The factions I have so far are:
XCOM: The main force fighting the aliens. A clandestine global organization funded by global and regional powers that just take orders. Made up of the best and brightest of humanity, XCOM deals with cleaning up/stopping alien abduction runs, alien terror attacks, UFO incursions, miscellaneous alien-related odd jobs from the Council, and researching the invaders' technology to turn the tide of the war. The organization is kept in the dark about everything not related to the current task, and is totally subservient to the will of the Council; if the Council is displeased with XCOM's work or even falls apart, the organization loses funding, potentially to the point of no longer being able to function. Additionally, the aliens will very quickly learn of XCOM's existence, and wiping the organization out will be a high priority for them.
XCOM's Council of Funding Nations: A clandestine organization made up of representatives of various governments that provide the money and manpower XCOM needs to do its job. The Council has been significantly expanded from base XCOM EW and now has 46 members, each contributing what they can. On the surface the Council would appear to be a shining example of humanity putting aside differences and working together to face a common threat. The reality - unbeknownst to XCOM - is much bleaker; although many (particularly smaller) countries are acting in good faith, the powerful Western ones have a hidden agenda: let XCOM win the war, get as many alien gizmos from them as possible, and then crack down on multipolarity and usher in a Pax Americana to last 1000 years. As a result, there is much friction between the Western backers and those funding states wise to these ambitions. Behind the scenes Western representatives decry the inclusion of countries with "bad human rights records", "undemocratic regimes", and "ambitions to use XCOM-developed technology to wage war on the rules-based order"; Western opponents call out the hypocrisy and some try to fight it. Time will tell whether the Council can hold itself together, or if petty politics and public panic will derail the alien fighters' gravy train.
The Aliens: Led by beings known as the Elders, this species-diverse army is actively trying to get Earth under their control. The main goal is simple: find a species both physically and psionically capable of harboring the Elders' immense power before 1) the Elders die off and 2) greater horrors come to threaten the universe. The invasion can thus be thought of as a probing attack to test humanity's strength; unfortunately for the aliens, humans are a vengeful bunch that won't cooperate with a force that - for all they know - is on a genocidal planet-wide rampage.
The Eldritch Horrors: The greater horrors known to the Elders' empire have already arrived at Earth, but are much more in the background. Little is known about their motivations or goals, but it's frightening enough to send the Elders into a panicked search for a better body in hopes of living to fight another day. I'm thinking Cthulhu meets X-COM: Terror From the Deep?
EXALT: An opportunistic bourgeois secret society that seeks to use alien technology to take over the world. They are much more overt and honest about their ambitions than Western Council members, and they are willing to work with the Elders to achieve their goal. Of course, they'll betray the aliens the first moment they can, and the Elders know it (and will eliminate the opportunists the moment they step out of line.) Regardless, this collaboration with the aliens displeases the Council enough that XCOM has been tasked with investigating and eliminating these "traitors to humanity". (Because only America is allowed to use Blaster Launchers and UFO-derived aircraft to rule the world.) Rumors abound that such powerful figures as Mark Zuckerberg and Elon Musk are involved in the organization, but they're just rumors at this point.
Army and Council of the Global South: A parallel alien-fighting organization spearheaded by XCOM Council members disillusioned by typical Western opportunism. Comprised of countries being exploited/attacked by both the West and Elders. Some members are part of both XCOM and ACGS (including Russia, China, and Iran), others (such as Venezuela, the DPRK, and Syria) were rejected from XCOM but joined the ACGS upon hearing just what the West was up to amidst an apocalyptic global crisis. This organization is currently unknown to those not affiliated, even XCOM and the CIA; time will tell whether they get found out and what XCOM's Council subsequently decides to do with them.
ADVENT: The Elders' planned world order for when Earth is conquered, this organization currently exists only in the Elders' strategy books. If they get a foothold on Earth (such as through countries surrendering to the aliens), ADVENT will become a reality, operating under a fascist colonial system and serving as a launching point for further alien actions. The Elders' current human experimentation programs are partly devoted to creating human-alien hybrid supersoldiers to be deployed as ADVENT forces and personnel, looking human enough to not raise suspicion but also being totally subservient to the alien will.
I can make a post detailing important NPCs, as well; a comment will cover the countries making up both Councils. Ideas and critiques are welcome!
Commander
Tell me this is a bit