A 38-year-old woman with no significant past medical history presents with sudden-onset severe headache, confusion, and petechial rash. Blood pressure is 165/105 mmHg. Laboratory investigations show platelet count 45,000/μL, creatinine 2.8 mg/dL, hemoglobin 9.2 g/dL with schistocytes on blood smear, and normal PT/INR. A diagnosis of thrombotic thrombocytopenic purpura (TTP) is suspected. What is the most appropriate immediate next step in management?