Morrowind:Redoran or Telvanni and Hlaalu

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It's actually possible to be a member of House Hlaalu and one other house at the same time. If you join House Telvanni or House Redoran first, then slay Orvas Dren or convince him to allow you to become Hlaalu Hortator (you will do this for the Main Quest), you'll be able to speak with Duke Vedam Dren about the Camonna Tong, and receive the message, Yes, I heard that you were the Hortator of House Hlaalu. You could not hold that rank if Ovas Dren did not wish it. Since you already have some agreement with Orvas Dren, I will name you the new Grandmaster of House Hlaalu. Followed by a raise in Hlaalu rank which can be repeated for more free promotions.

If you check then, you'll see that you are a Hireling in House Hlaalu and can do the quests, although some conflict, like e.g. Odirniran/Telvanni at Odirniran, where being in both Telvanni and Hlaalu you'll have to kill everyone there; also Rethan Manor will appear and it is required that you kill the owner of it. It is, however, impossible to join both House Redoran and House Telvanni without cheating or modding.

You can acquire two strongholds, but Vedam Dren won't issue you another contract, so you'll have to steal it from him then unbuild the Hlaalu stronghold via the console:

set stronghold to 0

NOTE: To avoid some confusion, you need to have heard of the topic Camonna Tong before this is possible. To access this, talk to Larrius Varro at Moonmoth Legion Fort and he will give you a quest looking for bad people. Then speak to most commoners about bad people and they will mention the name of the crime syndicate. Then you should be able to speak to the Duke.