The President nominates a number of judges that the Senate determines as necessary for them to deliberate through the advice part where they set all the parameters of the process and what constitutes a consensus choice, the President has no other role than providing that list of qualified and suitable persons, there is no confirmation, because that occurs after a choice is made by others, not by the Senate as required, because by and with are before and during, not after, so the check on those who serve in the judicial department is that judges serve during “Good Behavior”, and again the States in the Senate determine what constitutes good behavior and the manner of removal of any judge that violates that good behavior standard. Also, the Supreme Court does not decide which cases it will hear or will not hear, all cases the Supreme Court hears and decides are for petitions made for redress of grievances to Congress as the last resort on appeal, the Supreme Court is subservient to the States as the Union assembled in the Senate, and so is the President and the executive departments, so there are no coequal branches of government, and all checks and balances are legislative as part of the Article 1 mode of assembly of the States as a Confederated Republic in a bicameral legislature, which creates an iterative consensus choice legislative process to balance the interest of the Large and Small States by requiring the concurrence of the large most populous States to identify and rank choices, then the concurrence of the small more numerous States to determine the prefers choice by a majority consensus of all the States as the Union. When the 9 largest States pass a measure out of the House with only their votes to form a proportional majority, then there are 41 States in the Senate to reject the measure and return it to the House for reconsideration, along with their objections, this iterative process continues until the STATES in the Senate do reach a majority consensus of all the States to constitute assent for the measure, this is why the President only has a conditional check on legislation, and the President must return the measure with the justification for the veto, which is also determined by congress what constitutes a valid justification, that too is to return the measure to the House for reconsideration, and if the President doesn’t meet the standard for justification of the veto, then the veto is ignored and becomes law as if the President didn’t act on the measure in the time allotted for a veto. I know this sound unusual, but the other lever that is at the disposal of the States as the Union, is that if the President does not comply with these conditions set by the Senate, then they can be impeached and immediately replaced with someone who will comply with those, and other, conditions set by the States assembled in Congress as the Union and Established Government Authority, the Union which makes our country the United States of America. There is no such thing as 3 coequal branches of government, and if you read Federalist #51 properly, Madison tells us that it is not possible to provide the different departments of government with the necessary powers to protect themselves from the usurpation by the others, and that in the Confederated Republic of the United States, the legislative authority necessarily predominates, and that they divided the legislature into two assemblies with different modes of assembly and different modes of action, which created two independent and simultaneously operating governing assemblies, an article 1 assembly to govern how the States interact with each other to form and maintain the Union through laws, and an article 2 assembly to govern how the States act together as the union to make the decisions of a free and independent state through treaties; levying war, concluding peace, contracting alliances, establishing commerce, and any other Acts or Things an independent state may by right do, which are the Rights each individual State was seeking when they signed onto the Declaration of Independence. The Constitution gives the Senate the authority to establish the court, which means that the States must agree with 2/3 of the States to determine all aspects of the court, and at the time the Constitution was written the agreed to process was established in Article 9 Clause 2 of the Articles of Confederation, and contrary to popular opinion, that prior agreement is still in force because nothing in the Constitution of the United States amends it except for the appointment of a Chief Justice to Preside over the Supreme Court, who does not participate in the decisions, and a pool of judges who serve during good behavior, from which 5 are chosen by lot to hear and decide the dispute or grievance, and that a list of nominees is provided by the President for the Senate to consider and choose a person to appoint when vacancies occur in that pool. I know you won’t look it up yourself, so I’m posting it below, find anything there for the assembly or function of the Supreme Court that was amended by the Constitution of the United States: [Article 9 Clause 2 AOC The united states, in congress assembled, shall also be the last resort on appeal, in all disputes and differences now subsisting, or that hereafter may arise between two or more states concerning boundary, jurisdiction, or any other cause whatever; which authority shall always be exercised in the manner following. Whenever the legislative or executive authority, or lawful agent of any state in controversy with another, shall present a petition to congress, stating the matter in question, and praying for a hearing, notice thereof shall be given, by order of congress, to the legislative or executive authority of the other state in controversy, and a day assigned for the appearance of the parties by their lawful agents, who shall then be directed to appoint, by joint consent, commissioners or judges to constitute a court for hearing and determining the matter in question: but if they cannot agree, congress shall name three persons out of each of the united states, and from the list of such persons each party shall alternately strike out one, the petitioners beginning, until the number shall be reduced to thirteen; and from that number not less than seven, nor more than nine names, as congress shall direct, shall, in the presence of congress, be drawn out by lot, and the persons whose names shall be so drawn, or any five of them, shall be commissioners or judges, to hear and finally determine the controversy, so always as a major part of the judges, who shall hear the cause, shall agree in the determination: and if either party shall neglect to attend at the day appointed, without showing reasons which congress shall judge sufficient, or being present, shall refuse to strike, the congress shall proceed to nominate three persons out of each State, and the secretary of congress shall strike in behalf of such party absent or refusing; and the judgment and sentence of the court, to be appointed in the manner before prescribed, shall be final and conclusive; and if any of the parties shall refuse to submit to the authority of such court, or to appear or defend their claim or cause, the court shall nevertheless proceed to pronounce sentence, or judgment, which shall in like manner be final and decisive; the judgment or sentence and other proceedings being in either case transmitted to congress, and lodged among the acts of congress, for the security of the parties concerned: provided that every commissioner, before he sits in judgment, shall take an oath to be administered by one of the judges of the supreme or superior court of the State where the cause shall be tried, “well and truly to hear and determine the matter in question, according to the best of his judgment, without favour, affection, or hope of reward: “provided, also, that no State shall be deprived of territory for the benefit of the united states.] All the States must participate in assembling the court because they have agreed to abide by the court’s decisions to resolve their conflicts, disputes, and grievances.

Supreme court justices are appointed for life, then do they retire? because if they are appointed for life then there is no chance for every president to appoint a SCOTUS judge isn't it so?.

Now 6 and 3 on the courts :( personally I think that the party of each of the members is important. This is the highest court in the US so there should be an even amount of judges so that neither party steers and it's impartial, but then there'd be the question of a tie breaker so this idea may not be plausible.

Can't supreme court justices be impeached and removed as well?