https://blogs.sas.com/content/iml/2017/02/13/run-1000-regressions.html
That document shows how to handle multiple X-variables, it is easily modified to also handle multiple Y variables.
As always, I point out that just because you CAN do this, it doesn't mean you SHOULD do this, and there are better statistical methods to handle multiple X and multiple Y than just brute force running all possible combinations. One such method is Partial Least Squares regression (PROC PLS).
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Paige Miller