Metatheatricality is represented in Volpone by the performances staged for the benefit of the other characters who want Volpone's wealth bequeathed to them. In Jonson's play, the performing characters talk about the performance they are staging for the other characters; they talk about the characteristics, success and failure of their in-play performance.
VOLPONE [to Mosca for doing such a good job in his performance with Corbaccio]
O, but thy working, and thy placing it!
I cannot hold; good rascal, let me kiss thee:
I never knew thee in so rare a humour. (I.1.1)
Metatheatricality is a type of metafiction. Metafiction was introduced as a concept in the mid- to late-twentieth century when it was at its height for a time (c. 1960-1980). Metafiction is a postmodernist conception.
Modernists believed that, following two world wars, people had lost connection with their essential humanity and with the essence of nature. They understandably felt so, since World Wars I and II ravaged the face of the planet and shocked the souls of humans with devastating new war technologies, strategies, and machines of death.
Yet modernists believed there was hope of reclaiming the human soul and re-creating the connection with Earth, even though it was torn to bits and both people and earth were uprooted. Postmodernists, on the other hand, who came later, felt there was no such hope. They felt people were domed to continue to be alienated from their humanity and disconnected from the scarred earth. They chose to cope with this two-fold alienation by turning to the unreal: if they can't talk about truth and reality because they are alienated from both and can't understand either, then they'll talk about what is unreal.
The unreal they talk about in their fiction is the unreality within their fiction. Their stories have unreal characters, unreal plots, unreal settings, unreal conflicts, so they chose to turn their attention to pointing out various aspects of these unrealities. Metafiction is fiction which addresses its own fictionality: minor example, "Did you catch the foreshadowing there? Because I wouldn't want to be in his position with this conflict brewing."
You can see from this definition of metafiction that it is out of place to talk about Jonson's play as metafiction. Though Jonson was peeved with the cultural weaknesses of his day, there was no sense of human alienation from self and world, nor was there any desperate attempt to find connection with truth and reality.
Yet, if the idea of metatheatricality is taken in its broadest sense, it appears in Volpone in the interior performance put on as a way of swindling and duping those who wished to swindle and dupe Volpone.
Volpone has no family to leave his wealth to, only his trusted servants, like Mosca, to whom he gives great gifts. Socialites come bringing him gifts of wealth in hopes he will bequeath all to them. Volpone and his servants deceive them by putting on a charade to make them think he is in his last days to encourage their gift giving.
I have no wife, no parent, child, ally,
To give my substance to; but whom I make
Must be my heir: ...
This draws new clients daily, to my house, ...
That bring me presents, send me plate, coin, jewels,
let him enter.
Now, my fain'd cough, my pthisic, and my gout,
My apoplexy, palsy, and catarrhs, ...
Wherein, this three year, I have milk'd their hopes. (I.1.i)