So in each of your REG and LOGISTIC runs you should be getting some p values (I don't know whether these regressions have multiple predictors or not, but for now let's assume that they are univariate). Using ODS output you can get these into datasets. Then it is just a matter of shaping the datasets, setting them together, and running PROC MULTTEST.
From REG, look at the tables named ANOVA (for a p value for the whole model) and ParameterEstimates (for p values for individual parameters). From LOGISTIC, look for ModelANOVA (for p values related to the whole model) and ParameterEstimates (for p values for individual parameters). After identifying the correct row, you need to keep the p value, and some identifier. That would give you a dataset that looks like the one in the example, where the identifier is called Test1, Test2, etc.
Then comes the difficult part (at least for me) and here following @PGStats advice is critical, selecting the appropriate adjustment method.
SteveDenham
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