What do you mean by 'non-additivity?'
I suspect that it means the presences of effects in the response that are not only the additive main effects. If that guess is correct, then include cross-terms to test for interactions.
I am trying to see of the 3 factors are additive in the model.
Do you mean through running a full factorial ANOVA including 2way and 3way interactions, if any of the interactions terms are significant, the additivity of the three factors are not accepted ?