Although removing the Senate filibuster and 'packing the court' by adding extra seats has been suggested by some Democratic party activists, Biden is widely understood to be opposed to such measures and has not shown any support for them.
In 1869, Congress increased the number of justices on the Supreme Court from seven to nine. Republicans who controlled Congress were battling President Andrew Johnson (a Democrat who had assumed office when Lincoln was assassinated), and they sought to deny Johnson any appointments to the Court. By 1869, Ulysses Grant, a Republican, had replaced Johnson, and Congress expanded the number of justices from seven to nine. Therefore, the claim by President Trump cannot be termed as true.