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Isolated system will preserve its entropy unchanged (for fully reversible system) or it will increase its entropy (for system with irreversible processes).
For a closed system, it can receive energy in form of heat. Does this always imply, that its entropy will be below maximum? Is it possible to add heat in such a way, that entropy will remain unchanged and maximum?
I am not quite sure what you mean about "keeping the entropy below maximum", but most basic application of entropy is to determine, which processes are reversible.
As for reversible processes, you actually can add or remove heat in a way that the entropy of the whole universe remains the same. This is possible when you add the heat to the system by isothermal process (constant temperature). In fact, in isothermal process the change in entropy of the closed system will be opposite to the change of entropy to the rest of the universe. All other types of heat exchange increase the entropy of the whole universe.
That is the point of the Carnot process, in which you have two adiabatic processes (no exchange of heat) and two isothermal processes (constant temperature). Carnot process is fully reversible, thus it does not change the entropy of the universe.
If this is not exactly the answer you are looking for, please be more specific.
