Happy to edit the wiki, but would like to get all of the info straight first!
Here's my distillation of your investigation above, please can you verify?
Concubinage & government:
--- Tribal government only enables concubinage if you have CM or HL.
--- Nomads are only playable with HL, which enables concubinage for them.
--- Feudal/MR will not have concubines, unless granted by their religion.
--- If your religion has polygamy and your government has concubinage, then the concubinage from your government takes precedence - you will have concubines, not polygamy.
--- Speculation: If a modded government enables concubinage, then it will only work if the player has CM or HL.
--- Check: Does a Muslim tribal ruler without CM or HL have concubinage or polygamy? If my speculation/understanding is correct, I expect they have polygamy.
Concubinage & religion:
--- As an alternative, concubinage can be enabled by the character's religion, ie. by the DLC which make these religions playable. (HF/OG for pagans, OG/JD for Mazdan, RoI/JD for Eastern.)
--- Speculation: If a modded religion enables concubinage, then it will work even if the player has no DLC.
A few extra tests I can think of (I can't check right now, but can do some tests later today):
- Can a religion that does not normally have concubines get them with Random World Doctrines with only HF? It might not work consistently with modding them in for a new religion since it is unlocked after the game starts.
- Societies can grant the ability to take concubines (vanilla does not make use of this, but it can be modded in); how does that interact with DLCs? I would imagine it has not been as extensively tested by the devs as something that is used in the unmodded game.
- Does adding concubines with script commands (during gameplay) to e.g. a Catholic Tribal ruler work without the DLCs activating it for tribals? Does the "Concubine automatically set aside without opinion penalty on unpause" issue crop up when doing this? I expect it to work as if a ruler had them scripted in the history files.
- Does anything weird happen for courtiers with concubines based on active DLCs? Does that happen both with religion-based concubines and government-based ones, and does the liege having either have an impact (e.g. Norse courtier in a Catholic Tribal court, Catholic courtier in a Norse Tribal court, and Catholic courtier in a Catholic Tribal court)? Given that AI rulers seem to be able to have government-based courtiers even when they get automatically removed for the player, that could be a weird case.
- Is female and male concubinage consistently (un)locked by the DLCs that unlock them (for societies, governments, and religions)? Considering the ability for women to take consorts was added with 2.8/JD (or was it 3.0/HF?), older DLC unlocks might not properly account for it.
It might also be good to verify polygamy, because that might be broken in similar ways:
- Does polygamy work (for non-Muslims) with just HF (pagans and Random World rulers can pick a Doctrine for it, and you can also mod it in)? Meritocracy is broken without RoI (perhaps JD also works, because Taoists), if I remember correctly, so another broken Doctrine would not be entirely surprising.
- Can an unplayable religion have polygamy if you don't have SoI (and HF)? Muslims without SoI would be the only applicable vanilla religion, and I
think it works, but I have not played without either DLC since they were released...
- If the ruler has polygamy and a courtier has a religion that would unlock concubines, can the courtier have concubines regardless of DLCs (and does this work for both men and women)? I suspect they can.
- If a government unlocks the ability for women to take consorts but not the ability for men to take concubines, can a male ruler with that government marry multiple wives? Vanilla has no such government, so it is possibly an untested edge case.
- If a man with polygamy is in a society that gives men the ability to take concubines, does he have polygamy or concubines? If it works like governments, he should have concubines, but it might not be consistent.
- If a man with polygamy is in a society that gives women the ability to take consorts, what happens? Possibly an edge case.