There is no sensible answer to this question.
You can put any amount of charge on a blob of aluminum sitting in a vacuum, or surrounded by an ideal insulator. Why not?
If you put an awful lot of electrons on a blob of aluminum sitting in a vacuum, the electrons will eventually start shooting off by thermionic emission, and most of the excess charge will be gone after, let's say, 1 day. If you put even more electrons, most of them will be gone after 1 millisecond. But there is no "maximum" really, just a gradual speed-up of the discharging. Even 1 excess electron will not be stable for eternity.
If you subtract electrons instead of adding them, certainly nothing will happen. Well, I guess positively-charged atomic nuclei could fly off if the charge was significant enough. Again, this process does not let you say that a certain amount of charge is "the maximum possible", it's just a process that happens more and more frequently as the charge increases.
If you add or subtract an awful lot of electrons from a blob of aluminum surrounded by insulator, the insulator will eventually break down. If you have an ideal insulator that cannot break down, then nothing will happen no matter how many electrons are there.
You seem to have the idea that all electrons must come from surface atoms, so if you take away every electron from every surface atom, then it will be impossible to take away any more charge. But if you think about it, that's sort of a weird idea, when there's still all those electrons inside the metal! In fact, the idea is not correct. The "surface" where an insulator can store charge is not infinitesimal, nor necessarily exactly one atom thick. It's actually a depth equal to the so-called Debye length. If you subtract loads of electrons -- every electron from every "surface" atom -- the Debye length will just increase allowing you to scrape electrons out of atoms residing farther and farther from the surface.