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There is not a maximum amount of electrons that can be gained or lost by an atom, however, it would not be favorable to add 6 electrons to a Beryllium atom to get the octet. It would be easier for the atom to lose 2 electron to get this octet. For Oxygen, it would be the opposite. It is not favorable for the Oxygen atom to lose 6 electron to reach the octet, so it gains 2 electrons to get the octet instead.
If I'm understanding your question right, your asking what's the greatest number of atoms a central atom that's part of an expanded octet, where there are more than 8 valence electrons, can have. Most importantly, expanded octets have enough electrons to keep all atoms at the lowest possible energy for stability reasons. I think 10 is the maximum due to d orbitals, which cause expanded octets, having 10 electrons in them.
A good formula I found for the number of lone pairs of electrons on the central atom is LP= total Valence- 8*(number of other atoms that are not central) all over 2. So for example: ICl4 (-), total valence is 7+7(4)+1= 36. the central atom is I and there are 4 additional atoms that will be connected to it so by plugging into the formula you get; 36-8(4)/2= 2 Lone pairs of electrons on the central atom so now you know I will have 4 bonds and 2 lone pairs on it in the lewis structure. Hope this helps!
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