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In a polyatomic ion, the sum of the oxidation numbers of all atoms is equal to the overall charge on the ion. However, does this polyatomic ion have an overall oxidation number?

We also know that the oxidation number of a monatomic ion is the same as the charge of the ion, does the same apply for a polyatomic ion?

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Oxidation number has a meaning for atoms or monoatomic ions. It has no sense for polyatomic ions. A polyatomic ion has a charge. It does not have an oxidation number, although all its atoms do have an oxidation number

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  • $\begingroup$ "although all its atoms do have an oxidation number" and their sum should be equal to the charge of the ion. $\endgroup$
    – Karsten ♦
    Commented Sep 8, 2022 at 14:11
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TL;DR: A commentary on Maurice's answer.

We also know that the oxidation number of a monatomic ion is the same as the charge of the ion, does the same apply for a polyatomic ion?

This has one major gap in understanding. An oxidation state is defined for an atom, not a molecule. Look at the definition stated in the gold book[1],

Oxidation Number

In English is largely synonymous with oxidation state, and may be preferred when the value represents a mere parameter or number rather than being related to chemical systematics or a state of the atom in a compound.

Oxidation State

Gives the degree of oxidation of an atom in terms of counting electrons. The higher the oxidation state (OS) of a given atom, the greater is its degree of oxidation. Definition: OS of an atom is the charge of this atom after ionic approximation of its heteronuclear bonds.

Both of these definitions have one thing in common. It talks about the state of an atom not a molecule. Hence, there is no such thing as an overall oxidation number.

References:

  1. The IUPAC Compendium of Chemical Terminology. ** 2019. DOI: 10.1351/goldbook.
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If you consider the "overall oxidation number" of a polyatomic ion to be equal to the sum of the oxidation numbers of the atoms that make it up, then the overall oxidation number of a polyatomic ion is equal to the charge on the ion. For example: Nitrate has 1- charge. oxidation # for N plus 3(-2) for the three oxygens must equal 1-. For that to be true oxidation number of N must be +5. Sulfate ion has 2- charge. Oxidation number for S plus 4(-2) for the four oxygens must equal 2-. For that to be true the oxidation number for S must be +6

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    $\begingroup$ Overall oxidation number is something that does not exist. Oxidation number is the state of an atom within a molecule, and doesn't talk about the whole molecule. See Maurice's answer $\endgroup$
    – Safdar Faisal
    Commented Sep 8, 2022 at 13:47
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    $\begingroup$ This answer probably gave the OP the connection between charge and sum of oxidation states they were seeking. However, making up new terms in not a long-term strategy for communicating within a discipline. I think just giving the example and illustrating the the sum of oxidation states is equal to the charge would have been a better answer (of course, feel free to edit to improve the answer if you agree). $\endgroup$
    – Karsten ♦
    Commented Sep 8, 2022 at 14:14

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