A recent study on the topic of additivity addresses the task of search result diversification and concludes that while weaker baselines are almost always significantly improved by the evaluated diversification methods, for stronger baselines, just the opposite happens, i.e., no significant improvement can be observed. Due to the importance of the issue in shaping future research directions and evaluation strategies in search results diversification, in this work, we first aim to reproduce the findings reported in the previous study, and then investigate its possible limitations. Our extensive experiments first reveal that under the same experimental setting with that previous study, we can reach similar results. Next, we hypothesize that for stronger baselines, tuning the parameters of some methods (i.e., the trade-off parameter between the relevance and diversity of the results in this particular scenario) should be done in a more fine-grained manner. With trade-off parameters that are specifically determined for each baseline run, we show that the percentage of significant improvements even over the strong baselines can be doubled. As a further issue, we discuss the possible impact of using the same strong baseline retrieval function for the diversity computations of the methods. Our takeaway message is that in the case of a strong baseline, it is more crucial to tune the parameters of the diversification methods to be evaluated; but once this is done, additivity is achievable.