Can the US Supreme Court's appellate jurisdiction over cases in which it has original jurisdiction be limited?

Question

According to the US Constitution, the US Supreme Court has original jurisdiction in "all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party". Original jurisdiction of the US Supreme Court cannot be limited (nor expanded) by the US Congress, but the appellate jurisdiction can.

My understanding is as follows: the US Supreme Court's original jurisdiction is not necessarily exclusive, and thus other courts can also have original jurisdiction over these cases, which is known as concurrent jurisdiction. The plaintiff can thus choose the court in which he files the lawsuit. If the plaintiff chose to start the case not in the US Supreme Court, but rather in another court having original jurisdiction, then the US Supreme Court could have only appellate jurisdiction over such case.

Is it correct?

If so, could the US Congress strip the US Supreme Court of appellate jurisdiction over cases over which the US Supreme Court has original jurisdiction?

Edit: In an already deleted answer, It was argued that SCOTUS' original and appellate jurisdiction is mutually-exclusive, according to Marbury v. Madison. However, it seems that SCOTUS has rejected this argument in Cohens v. Virginia in which SCOTUS held that "where the words admit of appellate jurisdiction, the power to take cognizance of the suit originally does not necessarily negative the power to decide upon it on an appeal, if it may originate in a different Court" and "The general expressions in the case of Marbury v. Madison must be understood with the limitations which are given to them in this opinion".

Answer 1

This is an interesting question that, to the best of my knowledge, has never presented itself.

The statutory limitations on the appellate jurisdiction of the U.S. Supreme Court are very narrow and to my knowledge, there has never been an attempt to limit it with respect to matters of which it has original jurisdiction as well.

To make it a bit more concrete, one class of orders which is not appealable in federal court jurisprudence is an order remanding a case that is removed to a federal court back to its state court of origin. The reasoning behind this rule is that if there is concurrent jurisdiction, there is no legally cognizable harm in doing so in the judgment of Congress, and if the state court lacks jurisdiction, then the lack of jurisdiction can be appealed in the state court action and a new federal case can be commenced in a court with jurisdiction over the case.

If SCOTUS decided that a limitation on its appellate jurisdiction in this case was unconstitutional, as a practical matter, no one else could overrule its decision, so, effectively, it would have to consent to the limitation.

A closely related unresolved question of constitutional law is whether Congress has the power to deprive all courts of jurisdiction over some particular otherwise justiciable legal right necessarily established by the U.S. Constitution as an end run around amending the U.S. Constitution. Legal scholarship tends to suggest that this is not allowed, but Congress has not been bold enough to test this in a way that the courts interpreting laws in a manner to avoid constitutional questions, have had to resolve.

Answer 2

According to Article 3 of the United States Constitution vested the Supreme Court with appellate court jurisdiction in both law and fact.and granted congress the power to shape that juridiction.