Use dynamic programming with four variables to track the maximum profit after each buy and sell operation (buy1, sell1, buy2, sell2).

Initialize buy1 and buy2 to negative infinity (or a very small number) and sell1 and sell2 to 0, then iterate through the prices array to update these variables.

For each price, update the variables in the following order: buy1 = max(buy1, -price), sell1 = max(sell1, buy1 + price), buy2 = max(buy2, sell1 - price), sell2 = max(sell2, buy2 + price). The final answer will be sell2.