Hickam's dictum ("a patient can have as many diseases as he damn well pleases") has been touted as a counterargument to Ockham's razor, which enjoins clinicians to seek a single, simple, or unifying diagnosis. Yet the phenomenon of multiple diagnoses has not been formally analyzed. We evaluated multiple diagnoses using three methods of inquiry: (1) a review of 83 case reports; (2) a review of 220 cases from the New England Journal of Medicine; and (3) an online survey of providers' intuitions. Eighty-three published case reports claimed to instantiate Hickam's dictum or violate Ockham's razor. All reported a primary diagnosis that explained the presenting illness, and one or more additional diagnoses which could be classified into four categories: (1) an incidentaloma (n = 21; 25.3%); (2) a pre-existing disease (n = 26; 31.3%); (3) a disease causally linked to the primary diagnosis (n = 33, 39.8%); and (4) a causally unrelated second disease contributing to the acute presentation (n = 3, 3.6%). Among 220 cases from the New England Journal of Medicine, all reported a unifying final diagnosis. In an online survey, 265 respondents recruited using social media evaluated four hypothetical cases with multiple diagnoses representing this categorization scheme. A majority of respondents (79%; 95% CI, 74-84%) chose the case representing category 4 - a coincident, causally unrelated second diagnosis - as the most unlikely or surprising diagnostic combination. Multiple diagnoses commonly occur. However, the majority of the multiple diagnoses we analyzed were causally linked, or represented incidentalomas or known pre-existing diseases. These diagnostic combinations were unsurprising to a majority of surveyed providers. We show that multiple diagnoses can be arranged in a framework that considers time, probability, and causation. This framework reconciles the alleged conflict between Hickam's dictum and Ockham's razor and has greater practical and pedagogical utility.