A 52-year-old man is evaluated in follow-up. He was admitted to the hospital 2 weeks ago with a new diagnosis of acute myeloid leukemia. He has received induction chemotherapy with daunorubicin and cytarabine. Medical history is remarkable for an urticarial reaction to a platelet transfusion that resolved promptly with diphenhydramine. Other medications are posaconazole, valacyclovir, and cefepime.
On physical examination, temperature is 37.4 °C (99.3 °F), blood pressure is 132/72 mm Hg, pulse rate is 84/min, and respiration rate is 18/min. Oxygen saturation is 94% breathing ambient air. Oropharyngeal examination is unremarkable. He has scattered petechiae over both ankles and an ecchymosis at the insertion site of his central venous catheter.
Laboratory studies show he is neutropenic and has a platelet count of 12,000/µL (12 × 109/L).
Which of the following is the most appropriate management of this patient's thrombocytopenia?