Question

A $58$-year-old man is evaluated in the intensive care unit for worsening respiratory status. Eight days ago, he was intubated following a severe motor vehicle collision. Over the past $24$ hours, his oxygen requirements have increased, and he has developed a fever of $38.9^\circ\text{C}$ ($102.0^\circ\text{F}$). Copious thick, purulent secretions are noted in the endotracheal tube. Physical examination reveals coarse rhonchi over the right lung field. Laboratory studies show a leukocyte count of $16,500/\text{mm}^3$ with $85\%$ neutrophils. A chest radiograph demonstrates a new dense consolidation in the right lower lobe. The patient was empirically started on intravenous vancomycin, piperacillin-tazobactam, and amikacin.

Today, the quantitative endotracheal aspirate culture returns positive for $>10^5\text{ CFU/mL}$ of *Pseudomonas aeruginosa*. The isolate is susceptible to piperacillin-tazobactam, cefepime, meropenem, and amikacin. Blood cultures show no growth. His serum creatinine has increased from $1.0\text{ mg/dL}$ on admission to $2.3\text{ mg/dL}$ today.

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