Multiple studies and weak evidential defeat

When a study shows statistically significant correlation between an exposure and an outcome, the credence of a real connection between the two increases. Should that credence remain the same when it is discovered that further independent studies between the exposure and other independent outcomes were conducted? Matthew Kotzen argues that it should remain the same, even if the results of those further studies are discovered. However, we argue that it can differ dependent upon the results of the studies.