The most likely diagnosis is adult-onset Still disease (AOSD), a multisystem inflammatory disease characterized by high spiking fevers, arthritis, rash, high neutrophil counts, and markedly elevated serum ferritin. The rash is a nonpruritic salmon-colored macular/maculopapular rash on the trunk or extremities. Serum ferritin is elevated in many patients, often to extremely high levels, and is a marker of macrophage activation. Erythrocyte sedimentation rate and C-reactive protein can also be impressively elevated. Diagnosis is clinical, based on exclusion of infection, malignancy, or other rheumatologic diseases. Clinical criteria have been developed to assist in the diagnosis of AOSD. The most sensitive of these are the Yamaguchi classification criteria. Diagnosis requires fulfilling at least five criteria, two of which must be major. This patient fulfills three major criteria (fever, rash, joint involvement) and three minor criteria (splenomegaly, lymphadenopathy, elevated liver chemistries). Very few other diseases elevate ferritin to this level, although this is not currently one of the criteria.

Acute myeloid leukemia (AML) is a malignancy of myeloid progenitor cells. Clinical manifestations of bone marrow failure develop over days to months and include fatigue, dyspnea, and easy bleeding. Fever is commonly caused by infection. The leukocyte count can be low, normal, or high, but circulating myeloblasts are present in most cases. This patient has a significant leukocytosis but no circulating blasts, thus excluding the diagnosis of AML.

Granulomatosis with polyangiitis (formerly known as Wegener granulomatosis) is also a multisystem disorder characterized by upper respiratory, lower respiratory, and kidney involvement. More than 70% of patients have upper airway manifestations such as sinusitis or nasal, inner ear, or laryngotracheal inflammation. This patient has none of these manifestations.

Systemic lupus erythematosus (SLE) is also a multisystem disease with early nonspecific constitutional symptoms, including fever, fatigue, and weight loss. Common presentations include a photosensitive rash and symmetric polyarthritis. Cytopenia is common, whereas leukocytosis and extremely elevated serum ferritin levels are not characteristic of SLE.