Multivariate logistic regression?

Hi!

With my master thesis project, I only use categorical data. I have one independent variabele, with four categories. My dependent variables are dichotomous (yes/no). I would like to use logistic regression to calculate the odds that when the categories of my independent variable are available, the independent variable will be present or not. I already succeeded so far. However, my dependent variables are psychological symptoms, so I have over 40 of them. If I perform logistic regressions for every symptom (dependent variable) one by one, the error will be big. Therefore, I would like to use one statistical test to predict multiple dependent variables at the same time. I know this is possible using a MANOVA, however, for a MANOVA the dependent variable needs to be at the ratio/interval level, which is not the case. So, I am wondering whether there is a possibility to make my multiple regression multivariate as well?

Kind regards,
Daniëlle (a desperate student)