The Founding Fathers reached consensus that republicanism contains a provision to abolish and reform the government under new foundational laws, and is embodied in Article 4, section 4 of the Constitution. The means to do so exist through amendment, Convention or revolution, and the authority to do so resides in the people. For more on this topic I refer you to The Federalist Papers, No. 78
Here are the 7 small "r" republican principles that came out of the Constitution ratifying process, undefined but assumed in Article 4 of the Constitution:
The mechanism for that could be amendment or Constitutional Convention or revolution, and is expressly mentioned in 39 of the states' constitutions.
[M]ost State Constitutions include articles in the Declaration of Rights which reserve to the people the right to establish a new government whenever the government oppresses the people. The Maryland Declaration of Rights in Article 6 states, “That all persons invested with the Legislative or Executive powers of Government are the Trustees of the Public, and, as such, accountable for their conduct: Wherefore, whenever the ends of Government are perverted, and public liberty manifestly endangered, and all other means of redress are ineffectual, the People may, and of right ought, to reform the old, or establish a new Government; the doctrine of non-resistance against arbitrary power and oppression is absurd, slavish and destructive of the good and happiness of mankind.”
The Unanimous Declaration Reads:
[W]henever any Form of Government becomes destructive of these ends [to secure the inalienable rights to life, liberty and property], it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
The Massachusetts Constitution of 1780 (still in effect) reads:
[T]he people alone have an incontestible, unalienable, and indefeasible right to institute government; and to reform, alter or totally change the same, when their protection, safety, prosperity and happiness require it. (Declaration of Rights, Art. VII)
The State of Maryland Constitution’s first Declaration of Right still reads:
[The People] have, at all times, the inalienable right to alter, reform or abolish their Form of Government in such manner as they may deem expedient. (Declaration of Rights, Art. I.)
The State of New Hampshire ostensibly acknowledges in its Constitution:
[W]henever the ends of government are perverted, and public liberty manifestly endangered, and all other means of redress and ineffectual, the people may, and of right ought to reform the old, or establish a new government. The doctrine of nonresistance against arbitrary power, and oppression, is absurd, slavish, and destructive of the good and happiness of mankind. (Part First, Art. 10.)
That same phrase, “the doctrine of nonresistance against arbitrary power, and oppression, is absurd, slavish, and destructive of the good and happiness of mankind,” is found in both the Maryland and Tennessee Constitutions.
Constitutions of 15 States acknowledged the right of the People to alter or abolish the existing government when it becomes destructive to the ends for which it was instituted. See Pennsylvania Const. of 1873, Art. I, § 2; Maryland Const. of 1867, Dec. of Rights, Art. I; Virginia Const. of 1902, Art. I, § 3; Alabama Const. of 1865, Art. I, § 2; Arkansas Const. of 1874, Art. II, § 1; Idaho Const. of 1889, Art. I, § 2; Kansas Const. of 1858, Art. I, § 2; Kentucky Const. of 1890, Bill of Rights, § 4; Ohio Const. of 1851, Art. I, § 2; Oregon Const. of 1857, Art. I, § 1; Tennessee Const. of 1870, Art. I, § 1; Texas Const. of 1876, Art. I, § 2; Vermont Const. of 1793, c. 1, Art. 7; West Virginia Const. of 1872, Art. 3, § 3; Wyoming Const. of 1889, Art. I, § 1. Some 24 other States have, or have had, slightly varying forms of the same provision. See New Hampshire Const., Pt. I, Art. 10; Massachusetts Const., Part the First, Article VII; Connecticut Const., Article First, § 2; New Jersey Const., Art. I, 2; Delaware Const., Preamble; North Carolina Const., Art. I, § 3; South Carolina Const., Art. 1, § 1; Rhode Island Const., Art. I, § 1; California Const., Art. I, § 2; Colorado Const., Art. II, § 2; Florida Const., Dec. of Rights, § 2; Indiana Const., Art. I, § 1; Iowa Const., Art. I, § 2; Maine Const., Art. I, § 2; Michigan Const. of 1835, Art. I, § 2; Minnesota Const., Art. I, § 1; Mississippi Const., Art. 3, § 6; Missouri Const., Art. I, § 3; Montana Const., Art. III, § 2; Nevada Const., Art. I, § 2; North Dakota Const., Art. I, § 2; Oklahoma Const., Art. II, § 1; South Dakota Const., Art. VI, § 26; Utah Const., Art. I, § 2.12
Note the history of how the Articles of Confederation were replaced through a motion and Convention, and serves as a historical precedent.