A 28-year-old man from Delhi presents with a 10-day history of sustained fever (39.5°C), headache, myalgia, and rose spots on the trunk. Blood culture is positive for Salmonella typhi. He is currently on ceftriaxone 2 g IV 12-hourly. On day 3 of therapy, his fever persists, and he develops altered mental status with neck stiffness. What is the most appropriate next step in management?