Whothe faction that took a Cadian world — a Chaos, xenos or traitor gang that holds ground Cadia once held (any such gang; the Regiment's natural nemesis)
Termscampaign-level feud: while the feud stands, Cadia gains bonus reputation for a win against the enemy but the enemy's presence on the world is a running penalty until one side is driven off — the grudge of a world that fell
Cadia's oldest grudge is against whoever took one of its worlds. Any Chaos warband, xenos host or traitor gang that holds ground Cadia once held becomes the Regiment's natural nemesis — a broken-world feud carried at the campaign level. While the feud stands, Cadia gains bonus reputation for a victory against that enemy, but the enemy's continued presence on the world is a running penalty on the Regiment until one side is driven off for good. It is the grudge of soldiers who watched a world fall and mean to take it back: no truce, no forgetting, only the long work of reclamation.
The Manpower Reservoiralliance
Whoan allied Imperial force that requisitions Cadian troops — the Inquisition (drawing Veteran Guardsmen + Tempestus Scions) or a Genestealer Cult's mortal wing (drawing the Brood-Brother rank-and-file); any such faction, phase-gated
Termscampaign-level requisition pact: while it stands, Cadia may second a Veteran Guardsman or rank-and-file body to the ally between battles for a reputation return; the ally may field that unit as its own, and Cadia gains a favour in exchange — the Regiment seconded to a campaign, not a fixed pairing
Cadia is the manpower reservoir of the Imperium, and it allies by requisition rather than by oath. An allied Imperial force — the Inquisition drawing Veteran Guardsmen and Tempestus Scions, or a Genestealer Cult's mortal wing drawing the Brood-Brother rank-and-file — may call on Cadian troops through a phase-gated pact. While it stands, Cadia may second a Veteran Guardsman or a rank-and-file body to the ally between battles for a reputation return; the ally fields that unit as its own, and Cadia gains a favour in exchange. It is the Regiment seconded to a campaign, not a fixed friendship — line troops lent where the Imperium needs them, and recalled when it does not.