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If you put a unit that has an invul save, say 5++, into the save bubble of a Void Shield Generator (4++), does it get 2 invul saves of 5++, followed by 4++ if the first one failed?
The general rule is that you only get to take one armor save (the best one available to you usually). So unless there is some special rule that allows you to use the 4++ in addition to your normal save you would just take the better option (in this case the 4++)
The first one (+) is a normal armor save. It can be modified by things like AP or special abilities. The second one (++) is an invulnerable save. There are a very few things that can modify it. The third one (+++) isn't really an armor save. It usually represents something that can negate a wound or wounds. Things like Nurgle's disgusting Resiliance or Feel No Pain.
You can use the third set after failing an armor save since it applies to the wounds you take and not whether you are wounded or not (which is what armor does).