When it rains, it pours

In 17th- and 18th-century England, milkmaids had a reputation for having pretty faces. This was because they rarely seemed to get smallpox, which left pockmarks on the skin of its survivors. Milkmaids did, however, catch from their cows a milder, related disease known as cowpox. English physician Edward Jenner famously hypothesized that the milkmaids' contracting cowpox made them immune to smallpox. Using this observation, he successfully created the first vaccine. This is where we get the word "vaccine": in Latin, vacca means "cow."

And so, having a disease (cowpox) sometimes protects you from another (smallpox). For example, getting oral herpes can sometimes offer slight protection against genital herpes. Although being born with no spleen (congenital asplenia) can cause problems, it does eliminate the chance of a ruptured spleen (which can be a life-threatening complication of a motor-vehicle accident).

Unfortunately, the opposite usually holds: most diseases simply invite more disease.

• Myasthenia gravis is a disease of muscle weakness. Some patients have difficulty swallowing (dysphagia) and aspirate their food, leading to pneumonia. 
• Untreated gonorrhea inflames the lining of the vagina in a way that makes a woman more susceptible to HIV infection. 
• Hypertension, diabetes, tobacco use, and smoking all lead to a host of ills.
• Being in the hospital exposes patients to a whole host of nosocomial (hospital-acquired) infectious diseases, like C. difficile, a bacterium that causes persistent diarrhea. 
• Autistic patients are more likely to have nutritional deficiencies because they tend to be picky eaters.

For the most part, "when it rains, it pours."

This used to depress me, but I've started seeing it differently. If I can diagnose a disease promptly and treat it appropriately, the patient will stand less of a risk of contracting the additional diseases that may follow. It's like a two-for-one.