I had not intended to do a page for this, but there have been enough people on the Morrowind boards asking "how can I get more than one stronghold" that it seemed prudent to write it.
The short answer is that you cannot have more than one stronghold without running a plugin. I believe there is one out there that lets you do this, but it cannot be done without one.
The long answer is that there are a few very good reasons for this. First, you can only belong to one Great House. Yes, I know about the scripting bug with Duke Dren, but it is fixed by now so the original statement stands: you cannot belong to more than one Great House. Since you have to belong to a House before you can build a stronghold for it, you're stuck.
Second, regardless of your House, each of the stronghold quests starts with your going to see Duke Dren and obtaining a construction contract. This is purely a formality. All you have to do is ask for it and promise to be a nice person and the Duke will hand over the contract. However, there is only ONE construction contract and each stronghold that you try to build requires a contract. If you go back to ask for a second or third one, the game checks your journal to see whether it has already been given. If it has, you get a "sorry, but I've already given it to you" message and without the contract,
The third problem is continuity. At some point in your House career, you are going to have to go take out the owners of the two opposition strongholds. This will do wonders for your reputation and standing in the House that sent you out, but do terrible things to your reputation and standing in the other Houses. Each stronghold has an NPC who is nominally in charge of the place. That NPC is present, but inactive, in your stronghold because you are supposedly in charge. Unless you time it precisely, you're going to kill the NPCs and then have no one to kill when it comes time to do the equivalent quest(s) for the other House(s). Strictly speaking, in order to honestly complete the quests, you would have to kill yourself.
So do yourself a favor. Be content with a single stronghold. Considering that the strongholds are basically in the middle of nowhere, I don't see them as worthwhile for anything other than gaining rank in one of the Houses. If Bethesda had done something like put the strongholds in a town somewhere, I might be singing a different tune.