According to the Constitution, what power does the president lack regarding the Supreme Court justices?

The power that the president lacks regarding the Supreme Court justices is the authority to increase the number of justices. The Constitution does grant the president the power to nominate justices and appoint them with Senate approval, as outlined in Article II, Section 2. However, the number of justices on the Supreme Court is determined by Congress, not the president. This means that while the president can suggest nominees for vacant positions, he cannot unilaterally decide to add more justices to the Supreme Court; such a change requires legislation enacted by Congress. This separation of powers ensures that no single branch can unilaterally alter the structure of the judiciary, maintaining a system of checks and balances.