Do you try to run the Linden Lab client twice? I don't try to have an alt on simultaneously that way, I use an alternate viewer for the alternate. :-)

The best combination I have found so far is to log off completely then log the alternate on using the Electric Sheep viewer (ONREZ). After he's all rezzed and squared away I log on using the LL viewer. If I do it the other way around I lock up or crash eventually, but as long as I don't have long draw distances set in either client, and don't wildly move the camera all around and freak out the video card, I can keep both going indefinitely.

There is also another viewer that uses most of the Windlight features if you want that with both, but in my case, since Caliburn takes all the pictures, it doesn't really matter if the companion is using a plain-old vanilla viewer.