I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I want to test four hypotheses. The dependent variable is some sort of "quality" indicating variable. As quality is a highly subjective term, researchers have brought forward 10 different ways of quantifying the quality variable I am interested in. I consider each one of these valid and thus want to repeat the estimation 10 times for each of the different dependent variables (that are all assumed to measure the same concept, i.e. some quality notion). If at least one of ten of the respective p-values indicates significance, I infer that there seems to be a relation between the respective coefficient and the quality notion I am interested in.

**How do I adjust p-values in this case?**

Do I have to adjust them twice? One time given the fact that I test four hypotheses with one model and one time given the fact that I repeat the test ten times? If the former is true, wouldn't I always have to adjust any p-value in any multiple regression model?