Anti oxidants work on multiple targets, depending upon which class of anti-oxidants one is using. Their targets range from cellular, acellular (membranes, ECM, receptor or ligand proteins) to co-activators of oxidative pathways which they engage and neutralize.

Surely it's possible. See antioxidant systems are present in each and every compartment of the cell or tissue. Some are extracellular and some are intracellular, both enzymatic and non-enzymatic. Almost every cell of the body possess some antioxidant activity to neutralize oxidants produced in that particular cell. TNF-a being an inflammatory marker may also be directly or indirectly affected by antioxidant network.

m sure every cell of the body