I remember I was able to move Mudcrab into my house in Balmora. I forget the exact details on how I did it. I had posted the exact steps I took on the Xbox forums on the Microsoft site, and Microsoft has since deleted the entire Morrowind forum there. Thanks a lot, Microsoft!
Anyway, I do remember creating custom spells to cast on Mudcrab to make him follow me, and it was a bit of effort to get it all done.

Moving
Download a Spell from www.Tesnexus.com called ShinyFollowMe you can use it In Chameleon on any Creature or NPC Take them anywhere come in Handy if you want to put a dozen in the middle of Town to Gives the Guards some thing to Do has a Dismiss Spell as well