FDR tried it during his time, wanted to expand it to 13 I think. It didn't work. But what we really need for SCOTUS is time limits and automatic replacements at intervals to take politics out of the process a little bit.
There's a perspective from which FDR's attempt to pack the court did work: He didn't expand the court, but the credible threat that he would do so got the justices to back off on blocking the New Deal policies he was implementing.
We already periodically replace them, that period just happens to be their lifetime. If you shorten that period you lower the stakes if the "other side" gets to fill a slot, you'll get another chance to rebalance in X years, where X is a known value and doesn't require someone to die (or willingly relinquish power).