Increasing the oxidation state means that it would need to continue losing electrons. How to do that depends upon the "object" that you are wondering about, as there various oxidants that can be used. Can you be more specific?
"Rate of oxidation in an object" can be the speed at which wood is burnt in my fireplace, speed at which the fuel is consumed in a car engine, the speed at which battery works, or the speed at which I am burning glucose when riding on a bike (plus some).
Do you see why it is not possible to even try to answer your question?
Going through some terminology here may be of assistance for you. The term oxidation already implies a change by its very definition, so your question does carry a sort of roundabout meaning. I did still attempt to understand what you are trying to ask though. This term is probably best used in the context of atoms or molecules (not macroscopic objects).