Well you couldn't be Indoril in Morrowind but you could be the other two so...
But Indoril is also based in Morroind
I forgott to add the description of the three great houses in my last post so here their are
House Hlaalu:
Its main concern is business and profit. This is their great strength - they are fast talkers and intelligent traders - and their great liability; most Hlaalu are bribable, either with gold or with other favors, and their leaders are no exception. House Hlaalu retainers are also masters of thievery, sneaking, lock-picking, blackmailing and backstabbing, both literal and metaphorical. While some councilors will obviously be honest and fair, many are under-handed and corrupt.
House Indoril:
House Indoril is one of the initial six Great Houses of Morrowind. After being founded during the early part of the First Era, Indoril was one of the strongest Houses with vast political power and many Indoril nobles holding influential positions, due to its close ties to the Tribunal. It was the House of Chimer hero Lord Indoril Nerevar. Duke-Prince Indoril Brindisi Dorom ruled Mournhold during its destruction by Mehrunes Dagon.
Currently, House Indoril has no territorial holdings on the island of Vvardenfell. Indoril District occupies the heartland of mainland Morrowind, with lands south of the Inner Sea including the city of Almalexia or Mournhold, and the town of Necrom on the eastern coast with its City of the Dead. Indoril territory borders House Dres and the Deshaan Plain.
House Telvanni:
Traditionally isolationist, most House Telvanni of Morrowind wizard-lords pursue wisdom and mastery in solitude. But certain ambitious wizard-lords, their retainers, and clients have entered whole-heartedly into the competition to control and exploit Vvardenfell's land and resources, building towers and bases all along the eastern coast. The Telvanni think that wisdom confers power, and power confers right.House Telvanni was among the staunchest defenders of slavery, which they saw as an ancient Dunmer right. Their ideals and desires, evidently not concerning themselves, were left to the slaves to obey. However, both Khajiit and Argonians, the two most common slave races, could join House Telvanni and advance with the same level of respect as other races. Many of the towns, notably Sadrith Mora and Tel Aruhn, housed slave markets. Telvanni holdings were also worked by slaves, whereas the other Great Houses preferred to use generic workers. Telvanni were, therefore, strong enemies of abolitionists.