"That theory received a boost by recent research suggesting that the age at which a woman enters menopause—which is marked by a steep drop in production of the hormone estrogen—influences not only her risk for RA, but the severity of symptoms should she develop the disease." Arthritis Today - Menopause Increases Risk of RA
Reading that, I'd be taking phytoestrogens as soon as I realised I was heading into menopause. My mother started a phytoestrogen supplement which got rid of her menopausal symptoms. I have read phytoestrogens may also help to also reduce inflammation associated osteoarthritis and rheumatoid arthritis. I talked about phytoestrogens in more detail on another answer...
http://www.medhelp.org/posts/Thyroid-Disorders/can-I-use-wild-yam-cream/show/1955167
There are various genes associated with rheumatoid arthritis which include HLA-DRB1, CD40, CTLA-4, PTPN22. Genes associated with Graves include HLA-DR3, CD40, CTLA-4, PTPN22. HLA-Bw35 gene is also associated with severe Graves' eye disease and increased risk of gold toxicity with rheumatoid arthritis drugs.
"Graves disease is associated with pernicious anemia, vitiligo, diabetes mellitus type 1, autoimmune adrenal insufficiency, systemic sclerosis, myasthenia gravis, Sjögren syndrome, rheumatoid arthritis, and systemic lupus erythematosus.[2]" - Medscape - Graves Disease
"The frequency of another autoimmune disorder was 9.67% in Graves' disease and 14.3% in Hashimoto's thyroiditis index cases (P=.005). Rheumatoid arthritis was the most common coexisting autoimmune disorder (found in 3.15% of Graves' disease and 4.24% of Hashimoto's thyroiditis cases).
Relative risks of almost all other autoimmune diseases in Graves' disease or Hashimoto's thyroiditis were significantly increased (>10 for pernicious anemia, systemic lupus erythematosus, Addison's disease, celiac disease, and vitiligo)." - Pubmed - PMID: 20103030 - Prevalence and relative risk of other autoimmune diseases in subjects with autoimmune thyroid disease.