A 72-year-old man is evaluated for fever in the hospital after being on mechanical ventilation for 1 week for hypoxic respiratory failure due to influenza. After an initial period of improvement, his level of purulent sputum production has increased over the past 24 hours, and over the previous 48 hours it has been necessary to increase his FIO2 to maintain his oxygenation. His only medication is oseltamivir delivered by orogastric tube.

On physical examination, temperature is 38.3 °C (100.9 °F), blood pressure is 110/60 mm Hg, pulse rate is 115/min, and respiration rate is 18/min (ventilator set rate is 14/min). Pulmonary examination reveals diffuse crackles.

Laboratory studies reveal a leukocyte count of 18,000/µL (18 × 109/L), increased from 12,500/µL (12.5 × 109/L) 2 days ago.

Chest radiograph shows worsening pulmonary infiltrates.

Which of the following is the most appropriate next step in management?