Regression with some associated ordinal dependent variables

#1
I have some associated categorical dependent variables that are ordinal in nature (with 4 or 5 categories). If I want to see the effect of a set of independent variables (which can be both continuous and categorical) what is the right way to perform the regression?

Should that be a multivariate generalized linear model? Actually if I performed separate regression for each DV, I would use ordinal logistic regression. But as the variables are associated, I am afraid, that will be misleading to use in my case!

What should be the right procedure? Can SPSS handle this? A reference that I can follow is cordially expected.