You're barking up the wrong tree here, on a number of counts. The Romans had no such thing as a supreme court, had no body that was capable of taking on the constitutional functions of a supreme court, had no body that was capable of taking on the judicial functions of a supreme court, and had neither a concept of constitutional law in its modern sense or its juristic effects.

The Romans did not have a supreme court. Until the emperors began issuing rescripts, which appear to have been used almost exclusively for civil cases, there was no judicial body that had purview potentially over all aspects of Roman law, civil and criminal, in the way that the supreme court does. Roman courts assembled to try specific crimes, and therefore different charges were the responsibility of different bodies. There were dozens, if not hundreds, of courts in the forum, each responsible for a different set of charges. The sole possible exception to this is the people's assembly when assembled in a case of provocatio or appellatio--the distinction between the two terms disappeared over time, such that the jurists do not seem to know the difference anymore. When a defendant appealed to the tribunes and/or people to defend them against an unjust verdict (or, more typically, coercitio), the appeal could reach the people's assembly. However, this should not be thought of as a supreme court. Provocatio/appellatio had little relationship to the law in many cases: what was at stake was whether magisterial authority had been exercised excessively, not whether the initial verdict was wrong or unconstitutional. Therefore, the assembly did not rule based on whether the provisions of the law by which the charge had been made were valid or not, they ruled based on whether what had actually occurred in exacting justice from the defendant was within keeping of what the assembly considered acceptable behavior, whether it was technically legal or not. Furthermore, as Lintott has shown, there was no guaranteed procedure for provocatio/appellatio. Simply calling on the tribunes and/or people for aid against a magistrate was not sufficient cause for the case to go to the assembly. Lintott found a number of cases where the tribunes rejected the appeal, sometimes for years on end. Pleminius, charged with treason, appealed to the tribunes against his execution. The tribunes appear simply to have ignored his appeal entirely, resulting in the awkward fact that the appeal was technically still up in the air and therefore Pleminius could neither be executed nor retried: he eventually was caught up in a conspiracy to break him out of confinement and was for this reason at last executed for treason. There was, then, no clearly laid-out procedure for provocatio/appellatio that ensured that once a certain point had been reached constitutionally an appeal had to go through. And Lintott has showed that there was certainly no automatic provocatio/appellatio, and that instead the tribunes and/or people had physically to be invoked in order for anything to happen. Moreover, some types of crimes seem in practice, if not in law, to have been pretty much outside the realm of appeal. And it is no wonder, since provocatio/appellatio evolved from a "self-help" function of the people. The people's assembly, the tribunes, and the ability of both bodies to uphold an appeal against magisterial coercitio was originally the people helping themselves, coming to the aid of individuals appealing to them by absorbing them into mobs or, in the case of the tribunes, standing in the way. Only through the Conflict of the Orders in the early Republic had the people's assembly and the tribunes been recognized as binding bodies, and their functions and procedures often worked in somewhat odd ways.

This is relevant to the other reason why this question is going in the wrong direction, namely that constitutional practice did not exist at Rome. Now, this is something of an open question in the field at the moment, but a few things can be said for certain. First, the Romans had not written constitution. Many attempts--most successfully Lintott's--have been made to "reconstruct Rome's unwritten constitution," as Brennan puts it, in the weirdest use of the word "reconstruct" I have ever seen. But doing so is necessarily something of a made up task. The Romans did not have a constitutional document, and they did not really have "institutional laws," as you put it. In many, if not most, cases the institutions that ordered and governed the state were not established on foundations of law, but on the mos maiorum, which was not a consistent idea. This has led to a strong and growing trend in scholarship--it may even be the majority now, and I feel fairly confident in saying that it is probably the majority view among younger Roman historians--that we should not really be talking about Roman "constitutionality" in any sense, and that it is a constructed idea fabricated by Mommsen on the basis of the German federal state of his own time. In so many cases "constitutional" practice and law was only outlined post factum, or did not have any clear legal framework at all. For example, when members of the assembly cried out that thunder had been heard during a legislative assembly of Saturninus, they were hoping that Saturninus would dissolve the assembly because obnuntiatio, the announcing of unfavorable omens in the assembly, should cause the assembly to dissolve. But this is the first clearly historical use of the practice, and there appears to be no law regulating its use until the lex de agendo cum populo of Clodius in 58, which finally outlined clearly the procedure for obnuntiatio as a part of civil law. Saturninus simply ignored the announcement of bad omens: the expectation that he was supposed to follow it had no basis in law, and its legal status would not be clarified for another 40 years. Similarly, the famous struggle over leges de vi in the 60s and 50s. The use of political violence, while dating back to the Conflict of the Orders, had never been clearly defined in Roman law. There seems to have been an expectation, particularly among the plebs, that political violence could be used legitimately, but the circumstances and form of its use was not clear. Escalating violence and conspiracy had to be combated with whatever was legal procedures were on hand that might be considered relevant to the problem, and then post factum solutions were enacted legally. But these were not changes to an established constitutional habit, rather they should be understood as the creation of a body of regulatory law, such as what a constitution should have done in the first place if there had been one. By the end of the 50s the Romans appear to have been starting to come to grips with the insufficiency of this piecemeal approach (even the fairly large body of legislation introduced in 63 had not been sufficient, and much of it had to be rewritten), since during his consulship in 52 Pompey promulgated a series of institutional laws ranging from regulations on magisterial tenures in the provinces to a lex de vi. This cannot, however, be called a "constitution" anymore than Sulla's laws, often called Sulla's constitution. Like Sulla, Pompey merely defined or redefined a series of existing practices, sweeping in scope but nonetheless targeted to include those that he believed were a problem. Neither Pompey nor Sulla, nor indeed really anybody until the end of the civil war, was trying to establish a clear, constitutional basis for Roman institutions. For example, the senate was a traditional body that sat because of the mos maiorum--later laws regulated entry into the senate, the requirements for senators, and so forth, but there was never any attempt to render into law why exactly the senate sat and how, legally speaking, it was able to exist in the first place.

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