While the term multivariate, I now know, means analysis with multipledependentvariables a lot of people (like me) associate this term with more than oneindependentvariables (because the authors I read used it that way). Be careful not to get confused by responses by posters who misunderstand what you mean by multivariate.

I am not entirely sure what you are trying to do. If you want to know how independent predictors are related to a continuous dependent variable than linear regression works (or ANOVA). If you have a categorical dependent variable than, depending on how many categories it has and if they are ordinal or nominal, you would use some form of logistic regression.

I can't help with models simualtaneously predicting more than one DV as I don't know these methods. I do know that MANOVA and canonical correlations are two such approaches.