William Brennan, the great US supreme court justice, liked to greet his incoming law clerks with a bracingly simple definition of constitutional doctrine: five votes. “You can’t do anything around here,” Brennan would say, wiggling the fingers of his hand, “without five votes.”

Underscoring the truth of Brennan’s hardboiled definition was the court’s 5-4 ruling this week (with Chief Justice John Roberts in dissent alongside his three liberal colleagues) to let stand a Texas law that turns ordinary citizens into de facto bounty hunters empowered to sue anyone who performs or “aids and abets” an abortion on a woman past her sixth week of pregnancy. True, the single-paragraph unsigned majority opinion emphasized that in letting the Texas law take effect the court was not ruling on the statute’s ultimate constitutionality.

And yet. As Justice Sonia Sotomayor wrote in a passionate dissent, “Presented with an application to enjoin a flagrantly unconstitutional law … a majority of justices have opted to bury their heads in the sand.” President Biden powerfully joined those critical of the court’s decision. Declaring that the ruling promises to “unleash [..] unconstitutional chaos”, Biden promised to work to protect the constitutional right to abortion first recognized in Roe v Wade.

How might the president do so? Back in April, Biden empaneled a bipartisan commission of scholars, lawyers and jurists tasked with exploring the issue of “court packing”. The commission is scheduled to submit its report later this fall, which returns us to Justice Brennan’s five wiggling fingers.

There is nothing magical about the number nine, the present size of the supreme court. The constitution provides that there shall be “one supreme Court”, but says nothing about the court’s size or composition; these are matters left to Congress. In the early decades of the nation, Congress changed the number of justices six different times, from as few as five to as many as 10, before settling on nine in 1869. In 1937, Franklin Roosevelt, frustrated by a reactionary supreme court that resisted his New Deal initiatives, proposed expanding the supreme court’s bench to 15. Congress correctly rejected that court-packing plan as an attempt to manipulate the court to generate specific outcomes.

Biden, however, could now fairly and legitimately propose expanding the number of justices from nine to 11. Such an expansion would counterbalance the abuse of constitutional rules that enabled the confirmation of Neil Gorsuch and Amy Coney Barrett and the installation of the hardcore conservative bloc responsible for the Texas decision.

This is not to say the effort would be successful. Assuming Biden could find support in the House, expanding the number of justices would require Democratic senators to first eliminate the filibuster, something that Senators Joe Manchin and Kyrsten Sinema staunchly oppose. And we know that Republican lawmakers, led by Mitch McConnell, would accuse Biden of dangerously politicizing the court.

To which we may respond: pah-leeze. After all, it was McConnell who, in the wake of Antonin Scalia’s death nine months before the 2016 election, announced: “The American people should have a voice in the selection of their next supreme court justice. Therefore, this vacancy should not be filled until we have a new president.”

Armed with a rule of his own creation and a Republican Senate majority, McConnell flagrantly refused to grant a hearing to Merrick Garland, Barack Obama’s nominee to fill the supreme court vacancy ultimately filled by Trump’s choice, Neil Gorsuch.

But when Ruth Bader Ginsburg died, six weeks before the 2020 election, McConnell suddenly pronounced a new rule. It turns out the American people should not have a voice in the selection of supreme court justice in an election year when the incumbent president is a Republican.

The confirmation of Amy Coney Barrett did more than install a supermajority of conservatives in the court. The locus of power on the court shifted from the more mainstream conservatism of Justice Roberts to the more ideological and rigid extremes of Clarence Thomas and Samuel Alito.

As the Texas ruling underscored, this is a court far more conservative than the nation whose constitutional meanings it is meant to protect. And it is a court that owes its composition to the triumph of anti-democratic processes, in which a majority of its members were nominated by a president who lost the popular vote and/or were confirmed by a bloc of senators elected by a minority of voters.

In proposing the addition of two additional justices, Biden could hardly be charged with tit-for-tat politics or with further politicizing the court. Conservatives would continue to enjoy a 6-5 majority, but with Justice Roberts, a stalwart institutionalist, serving as the swing vote. Were Biden to succeed, such an expansion would make the court more legitimate, not less.

• Lawrence Douglas is the author, most recently, of Will He Go? Trump and the Looming Election Meltdown in 2020 and is also a contributing opinion writer for the Guardian US. He teaches at Amherst College