Word for the possibility of being many things at once

I'm searching for a term describing the possibility of an entity to be seen many different things at the same time. The general concept of being able to categorize an entity into several context-dependent abstractions.

A car is not only a car, but can be:

• A vehicle
• A toy
• A risk
• A pollutant
• A Faraday's cage
• A source of taxation
• A trap
• A tool
• A weapon

Words that does not capture the proper meaning:

• A car is flexible.
• A car is adaptable.
• A car is versatile.

Words that might work

• Multifaceted
• Multi-sided

I need a general noun for describing this property in a ontological context

• Multifacetedness (Does not sound natural)
• Multi-sidedness (Even less natural)

Let's try some sentences

You could be anything you want, [multifacetedness] is universal.

We are not allowing [multifacetedness] in this game, you can only be one thing at a time.

Philosophers all agree, [multifacetedness] is fundamental in how we perceive and make sense of the world.

Is there a better word for this?

Multiplicity might suit you. From Merriam-Webster's full definition:

multiplicity noun
plural multiplicities
1 a : the quality or state of being multiple or various
. . .
Shakespeare's works seem to encompass the full multiplicity of human experience.

Philosophers and psychologists do use this term, though perhaps not in exactly the way you want. See, for example, this question and its answers on the Philosophy StackExchange (content is above my pay grade, so I'm not clear on how closely this lines up with your ideas) and this entry on multiplicity on the Dissociative Association's website.

At least one psychologist appears to be thinking along your lines:

MULTIPLICITY presents an entirely new view of our selves. Instead of seeing each person as a single personality, Carter argues that we all consist of multiple characters, each one with its own viewpoint, emotions and ambitions. The mother who feeds breakfast to her children, for example, has quite different concerns and opinions from the woman taking part in a boardroom discussion two hours later, and from the woman she will be with her husband that night. Yet all three may share the same body, and none is any more "authentic" than another. (Amazon book blurb for Multiplicity: The New Science of Personality, Identity, and the Self by Rita Carter, bolding added.)

Note that this definition pertains more to how your car views its own many roles and identities, rather than how you or I perceive the car, but I think it could easily encompass both.

multifacetedness, multifaceted, multi- + facets

The real word for being multi-sided and thus having many facets is multifaceted, correctly spelled with an e not an i, and whose second, figurative sense Wiktionary gives as:

Having many aspects; nuanced or diverse.

Joanne was a multifaceted individual; she knew how to bargain both with Wall Street brokers and push-cart vendors.

I don’t where you came up with that weird spelling that nobody would be able to make any sense out of, because you have effaced the face part of it with your spelling error. In speech it would of course make no difference, but in writing you’ve lost the underlying root and so produced something confusing.

The OED attests multifacetedness as a noun derived from multifaceted, but I agree that it might come off as awkward; it is not an especially common word.

As I mentioned to the asker in a comment, I completely agree with him that I like the sound of neither multifacetedness nor multisidedness. One should always be wary of piling up ever-increasing suffixes to derive “new” words like this. It sounds really clunky, so if there’s a simpler word available, then one probably should. See also nominalization, which is sometimes useful but too often a hallmark of terrible writing and military bureaucracy.

I think the term that may fit your sentences is versatile or versatility:

• capable of or adapted for turning easily from one to another of various tasks, fields of endeavor, etc.:

The Free Dictionary

How about multifariousness?

mul·ti·far·i·ous: many and of various types; having many varied parts or aspects [Google search]

It's word that Nietzsche and Nietzsche scholars have used, especially in regard to Nietzsche's multifariousness of the self, i.e., of ones inner drives. Google "multifarious Nietzsche".