Jack,
I'm going to assume you are not interested in combining your 3 dependent variables into one "multiple variable" analysis for a mixed design MANOVA. If that were what you are thinking, take a look at this link for potential issues and strategies with that approach. Weaver, Bruce. (2021). Re: Mixed MANOVA in SPSS?. Retrieved from https://www.researchgate.net/post/Mixed_MANOVA_in_SPSS/60c110a40915b01fa569b0a3/citation/download.
Rather, I think you are looking for what's called a Mixed Design ANOVA. For each of your 3 dependent variables, you're going to want to setup its own a mixed measures ANOVA with your time of test as your within-subject variable (pre, during and post treatment), and any of your other variables (gender and race) as between-subject variables. Some examples of this and how to run the tests in SPSS can be found here. https://edge.sagepub.com/system/files/chapter15_1.pdf
I hope this helps. John