A 38-year-old woman is admitted to the medical ICU with acute hypoxemic respiratory failure. She was well and healthy until 4 days prior when she abruptly began to feel ill with fevers, chills, bilateral pleuritic chest pain, and worsening shortness of breath. She has no signifcant past medical history but has suffered the recent death of her father following a car accident. In coping with his loss, she began smoking cigarettes again after a 15-year period of abstinence. She has been smoking up to two packs of tobacco daily. After she began to feel ill, she started taking acetaminophen and pseudoephedrine but otherwise takes no medications. Upon arrival in the emergency department, her oxygen saturation was 78% on room air. On a non-rebreather mask, the oxygen saturation increased to 92%. The vital signs are as follows: temperature 38.7°C (101.7°), heart rate 122 bpm, respiratory rate 28 breaths/min, and blood pressure 132/82 mmHg. She appears in moderate respiratory distress. There are bilateral difuse crackles. The cardiovascular examination shows regular tachycardia without murmur. The jugular venous pressure is not elevated, and no edema is present. The abdomen is soft and not tender. No hepatosplenomegaly is present. Extremity and neurology examinations are normal. Chest radiograph shows difuse bilateral infiltrates. Her echocardiogram shows normal left heart systolic and diastolic function. She is treated with ceftriaxone 1 g intravenously (IV) daily and azithromycin 500 mg IV daily. Over the course of the first 24 hours, the patient’s clinical condition continues to deteriorate. She remains febrile, and she requires intubation and mechanical ventilation. The patient’s ventilator is set on assist control with a rate of 28/min, tidal volume of 330 mL, fraction of inspired oxygen (FiO2) of 0.8, and positive end-expiratory pressure (PEEP) of 12 cmH2O. On these settings, her arterial blood gas values are pH 7.28, PaCO2 68 mmHg, and PaO2 62 mmHg. A bronchoalveolar lavage is performed. The cell count shows 58% neutrophils, 12% lymphocytes, and 30% eosinophils. What is the best approach to the treatment of the patient at this time?