There is a treatment that cleans out the gunk: plasmapheresis. The antibodies are filtered out of your blood, and then your blood goes back in. It's similar to dialysis. That works very well for some people, but it's a pretty extreme treatment, and it doesn't stop your body from making more antibodies. So after six weeks or so, your all gunked up again. But it's good for emergencies, because it works so quickly.
Another treatment is IV immunoglobulin. This is sort of the opposite. You're infused with the pooled antibodies of donors. They use this treatment for people who don't make their own antibodies, but it also works for people like us with autoimmune diseases. No one's sure how it works exactly, but it may be that when your body sees it has plenty of antibodies, it stops making more for a while. Or it may be that the new antibodies bind the offending ones.
Immunosuppressant drugs (Imuran, CellCept, Prednisone, and others) work by suppressing your immune system so it will stop making the offending antibodies, or stop making so many of them.
I'm taking Imuran. It took over a year before I noticed a difference. I thought it would make me more prone to infections (like more colds), but it hasn't, at least not so far. I am worried about developing other autoimmune diseases in the future (I have MG and Graves), like rheumatoid arthritis or lupus, so as long as my body can tolerate the Imuran, I'm sort of glad to be on it. I don't know for sure that it will prevent me from getting more autoimmune diseases, but it seems like a reasonable conjecture.