The US Constitution does not require any specific number of justices at all. The US Constitution creates the Supreme Court but leaves it to the Congress to determine how many will be on the Court.
Since adoption of the Constitution, Congress has passed numerous laws changing the number of justices. The current number of nine has been fixed by statute ever since 1869. Prior to that the Supreme Court began with 6 at the Court's inception, then reduced the number to five, increased it to seven, then to nine, then to ten, then to seven again, and finally to its present day number of nine.
Congress may change the number of justices at anytime it wishes to pass the appropriate statute.
Presently Title 28 of the United States Code, Section 1, states that the Supreme Court shall consist of a Chief Justice and eight associate justices.
The last time a change in court size was seriously proposed was by Roosevelt in 1937 wherein he proposed a bill to pack the court with 6 additional justices of his liking. See "The switch in time that saved nine." A key swing justice, Owen Roberts, thereafter ruled in Roosevelt's favor and the bill was quietly dropped. From this attempt to adjust the courts size came some of the most far reaching decisions that shaped our society. Decisions about Japanese internment, wage, price, commodity controls and the rise of extra-constitutionally authorized federal agencies marked this far reaching but little known (outside legal circles) event.