I have been trying to decipher Trump and Giuliani's end game. Keep in mind that half of Republicans think Trump was the victim of massive voter fraud, and more than 1/4 think he should fight to the end. Republican leaders with something to lose still fear him.
Trump team's convoluted, disjointed legal arguments appear to be rooted in Bush v. Gore. The SCOTUS majority ruled that a lack of standard method for dimpled chads violated the equal protection clause. The decision apparently included this sentence: “Our consideration is limited to the present circumstances, for the problem of equal protection in election processes generally presents many complexities.”
In other words, they did not want it cited as a precedent, but I gather that is not stopping Giuliani et al. They are evidently arguing that a lack of standard application of rules concerning ballot curing violates the equal protection clause. As a remedy, they wanted the court to nullify the entire vote in PA.
A Republican federal judge dismissed the case. Trump plans to appeal. Meanwhile, the Trump campaign has tried other tactics, like trying to block certification of the vote in other states, such as Michigan, Arizona, Georgia, and Wisconsin. The idea is to drop Biden below the 270 threshold. Some say that would push the vote to the House; with each state getting one vote. Trump wins. Others say the threshold is lowered and Biden still wins.
Another approach is to try to get Republican state legislatures to override the popular vote in their states, and appoint Trump electors instead. My understanding is this is supposedly based on a "plenary power of the legislature" interpretation expressed by Chief Justice Rehnquist's concurring opinion, which was joined by Justices Scalia and Thomas.
Some ardent Trumpists believe the 3 Trump appointees will join Alito and Thomas in throwing out fraudulent elections and allowing state legislatures to appoint Trump electors. While extremely unlikely, that is at least remotely possible and would create a nightmarish scenario.
It's also possible that Trump's absurd behavior finally exposes him for what he is; part oaf, part third world dictator, and he fades into obscurity. Well, there are the criminal cases in NY, so maybe at best he becomes am annoying side show?
Most likely, Trump sets himself as de facto leader of the Republican Party, a sort of True President in exile, and does everything he can to undermine the Biden Admin -- with a 2024 run in mind. That is the most logical end game.