There are several rare forms of pneumonia, including:

1. Eosinophilic pneumonia: This is a group of rare infections that affect the lungs. It occurs when a type of white blood cell builds up in the lungs and blood, causing inflammation and damage. Causes include smoking, allergic reactions, and parasitic infections.

2. Chronic eosinophilic pneumonia: This is a rare disorder characterized by the massive accumulation of eosinophils in the lungs (pulmonary eosinophilia). Eosinophils are a type of white blood cell and are part of the immune system. They are usually produced in response to allergens, inflammation, or infection (especially parasitic ones) and are particularly active in the respiratory tract.

3. Atypical pneumonia: This is a type of pneumonia caused by bacteria that are hard to detect through standard bacterial methods. These "atypical" bacteria include Chlamydia pneumoniae, Chlamydia psittaci, Legionella pneumophila, and Mycoplasma pneumoniae. Even though these infections are called "atypical," they are not uncommon.

4. Mycoplasma pneumonia: This type of pneumonia has somewhat different symptoms and physical signs and is referred to as atypical pneumonia. It is caused by the bacterium Mycoplasma pneumoniae and generally causes a mild, widespread pneumonia that affects all age groups.

Its important to note that these forms of pneumonia are rare and may not be the cause of most cases of pneumonia. The most common types of pneumonia are bacterial, viral, and mycoplasma pneumonia.