Will there be Imperium vs Imperium? That might be tricky, but how's this for an idea?
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On an Imperial held world at the fringes of the Imperium a powerful pre-fall Eldar psychic artifact is discovered and accidentally activated.
If used properly, the function of this artifact is not just to open doors into the webway, but to fully create new tunnels in the webway that are large enough for full-blown strike cruisers to navigate.
Dark Eldar
The Dark Eldar have learned of this discovery, and cannot let such power fall into the hands of their enemies. If Chaos or the Imperium learn how to use this artifact to its full extent the Dark Eldar's single place of refuge from She-Who-Thirsts would be destroyed.
Whatsmore, the power this artefact would provide to a Cabal, Coven or Cult could instantly lift them to the upper echelons of Commoragh society...
Chaos
Meanwhile, Ahriman of the Thousand Sons has also heard of this discovery. In a bid to gain access to the Black Library he has sought out forces to retrieve this artifact. In his typical Tzeenchian way, he will not use his own to further his agenda. With promises of an entire realm untouched by disease or decay within their grasp within the webway, a powerful Nurgle Champion has answered his calls. As the war escalates, doubtless more warbands will flock to his cause.
Imperium
A note is passed to a member of the administratum. The heading reads 'Minor Disturbance on Fringe World'. Adjusting his optical implants, he skim-reads the report. 'Arcane device', 'forces of the enemy', 'ten million lives'. In the fug of incense that permeates the room, he stamps the requisition order for reinforcement and places it in the vac tube to send away for actioning.
Lightyears away, orders are scrawled by astropaths of the Imperial fleet and millions of troops are mobilised. Their orders: purge the heretic and the xeno. Destroy the device for the good of mankind at all costs.
However, even the forces of the Imperium are not united. The planetary PDF is both strong and fiercely independent being based so far from the core Imperial worlds. Through garbled orders from distant powers and sheer stubbornness they have so far resisted relinquishing control of the planet to the arriving Imperial reinforcements. Plenty of their members have experienced the readiness with which the Imperium orders exterminatus and will stop short at nothing to prevent that happening to their homeworld. Even open warfare against the Imperium itself.
Furthermore, a radical Inquisitor from the Ordo Xenos has requisitioned yet more Imperial forces in a bid to capture the device. The power it would give the Imperium over the fickle Eldar is considerable, and he is hell-bent on using the artifact. Not even orders from the High Lords of Terra is enough to sway him from his goal. Anything standing in his way will be subject to his wrath, allied or otherwise.
Tyranids
However, the activation of this artifact has had a consequence unknown to the other factions. The psychic thrumming of its powerful engines has pierced the empyrean and is bathing the planet in a steadily growing beacon of psychic energy. Unbeknownst to the other factions, this beacon is drawing Tyranids from lightyears around inexorably towards the planet like moths to a flame. As the power within the arcane device continues to grow, they will be drawn in in ever increasing numbers.
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How's that?