A 72-year-old woman with type 2 diabetes and hypertension is admitted on day 3 of COVID-19 with fever, cough, and SpO₂ 92% on room air. Chest X-ray shows unilateral right lower lobe consolidation. She is started on supplemental oxygen and dexamethasone. On day 5 of admission, her fever persists, SpO₂ drops to 89% despite 4 L/min oxygen, and she develops purulent sputum with elevated procalcitonin (2.8 ng/mL). What is the most appropriate next step?