Q:

Comorbidity of autoimmune diseases

Do people who have one autoimmune disease (for example rheumatoid arthritis, Crohn's, Hashimoto hypothyroidism) have a statistically significant higher chance of developing another autoimmune disease in another part of their body later in life? 

A:

Yes, there is statistically significant comorbidity with autoimmune diseases. 
The study Recent Insights in the Epidemiology of Autoimmune Diseases: Improved Prevalence Estimates and Understanding of Clustering of Diseases analysed other studies on the subject. It puts the comorbidity of 29 autoimmune diseases - including, for example, Crohn's, diabetes, rheumatoid arthritis - at around 7 to 9 percent. 
Earlier studies put the comorbidity number lower, at around 4 to 6 percent, this appears to depend mainly on what diseases are considered and the quality of the records being reviewed for the large population-based studies. 
They found that certain diseases "cluster" in patients, for example type 1 diabetes, rheumatoid arthritis and thyroiditis. The reverse is true as well, several of the analysed studies  report that rheumatoid arthritis in combination with multiple sclerosis occur together less frequently than expected. 
Two other main meta analyses on the subject are

Are Individuals With an Autoimmune Disease at Higher Risk of a Second Autoimmune Disorder? in the American Journal of Epidemiology
Autoimmune diseases co-occurring within individuals and within families: a systematic review in the journal Epidemiology

The conclusion that a significant comorbidity exists and that it's more prevalent between certain diseases is drawn by all these studies the studies, which is also discussed in the first paper I linked. 

