The United States and the several States can not hold a man's allegiance. The are both body politics. The principal was laid out by Lord Coke in the Case of the Postnati. This case is cited as authority in 400 plus State and Federal cases.
A body politique (being invisible) can as a body politique neither make nor take homage: Vide 33 Hen. 8. tit. Fealty, Brook. 5. In fide,94 in faith or ligeance nothing ought to be feigned, but ought to be ex fide non ficta.
There is also a second reason why there can be no allegiance to the States or the United States. That reason is the courts have held numerous times that the government has no individual duty of protection to any individual man. The duty of protection is the very nature of allegiance.
From the same case
between the Sovereign and the subject there is without comparison a higher and greater connexion: for as the subject oweth to the King his true and faithful ligeance and obedience, so the Sovereign is to govern and protect his Subjects, regere etprotegere subditos suos:.so as between the Sovereign and subject there is duplex et reciprocum ligamen; quia sicut subditus regi tenetur ad obedientiam, ita rex subdito tenetur ad protectionem: merito igitur ligeantia dicitur a ligando, quia continet in se duplex ligamen.
The footnote: a dual and reciprocal tie, because just as the subject is bound in obedience to the king, so the king is bound to the protection of the subject; and therefore allegiance is properly so called from ligando (tying) because it contains within itself a two-way tie.
That all being said there is nothing stopping you or the government to agreeing to the legal fiction that there is a sovereign subject relationship. This relation will be presumed by the courts unless specifically rebutted.
Also in regards to the Pledge of Allegiance, it is not mandatory. Even if it were a mandatory requirement it would not be binding because there are no mutual oaths and the schools stop making childern say the Pledge of Allegiance exactly when it would become binding. That would be at the age of 12.