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Suppose we have a capacitor charged with charge $Q1$
Then an electron beam hits the positive plate of the capacitor, thus increasing the charge of the capacitor (the battery will begin to deposit the electrons on the blue plate, thus increasing the charge such that $Q2> Q1$)
My question is, what is the maximum charge that a capacitor can support before it breaks?
That depends on the material used as a dielectric between the plates and the distance between them. Different materials are used as dielectrics depending on the capacitor and its intended use.
The dielectric material can be made from a number of insulating materials or combinations of these materials with the most common types used being: air, paper, polyester, polypropylene, Mylar, ceramic, glass, oil, or a variety of other $materials^1$.
The measure of how much the capacitance increases for the dielectric material is called the permittivity or dielectric constant.
Ref. 1 https://www.electronics-tutorials.ws/capacitor/cap_1.html
