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Is my interpretation correct that an Allied Detachment can never be the same faction as the Primary Detachment, which basically means no CSM + Black Legion, no Tau + Farsight, no Eldar + Iyanden, no SM + Sentinels of Terra / Clan Raukaan etc.? In friendly games this is a non-issue, since you can have multiple Combined Arms detachments, but it’s sounding like tournaments (including GW’s own tournaments), are restricting players to a single Combined Arms detachment! Argh!

Allied cannot have the same faction as the CAD. as suppliments have the same faction as the parent codex, ie Clan Raukaan is faction C:SM. the only exception is C:SM chapter tactics, as long as the CTs are diferent they can ally, although Clan Raukaan is still IH chapter tactics so cannot ally with an IH CAD.

Many US tourneys are allowing self-ally, despite the BRB

Allying with yourself is allowed.
Taking an Allied Detachment that has the same Faction as your Primary Faction is not allowed.

Want a cheap 25-point way to circumvent this?
Inquisitorial Detachment (Primary)
-Inquisitor
Combined Arms Detachment
-Tau Stuff
Allied Detachment
-Farsight stuff

Of course, then the Inquisitor has to be your Warlord...

And since they are Desparate allies... you can't benefit from his powers, or even come close enough to protect him.