Does the output from GLM > Multivariate only assume continuous dependent variables?

Yes, but you might consider Generalized Linear Models or Regression > Optimal Scaling. With the latter procedure, you can construct transformed variables that might be used in GLM Multivariate

Hi Jon, thank you for your response! Can you please clarify what your answer of yes is referring to?

1) Can you run multivariate multiple regression analysis with categorical independent and dependent variables; or 2) Does the output from the multivariate procedure in SPSS only assume continuous dependent variables?

Update:

My question now is how to run multiple-group discriminant function analysis in SPSS, since this statistical procedure appears to be the best fit for my data/research questions.

Yes refers to your original question.

If you want to run discriminant, it's under Analyze > Classify.

You might also want to look at Multinomial Logistic under Analyze > Regression

Thank you! Another follow-up question: With multinomial logistic regression, how can I add more than one dependent variable? (I have already done multinomial logistic regression with EACH dependent variable, but I would like to combine all of the dependent variables into one analysis to see whether responses across ALL dependent variables can be predicted by certain independent variables.)

My inquiry presently is the way to run numerous gathering discriminant work examination in SPSS, since this measurable strategy gives off an impression of being the best fit for my information/research questions.