Of course it is possible. Suppose u have A,B->C,D. A and B independent, C and D dependent
Multiple regression is an extension of simple linear regression in which more than one independent variable (X) is used to predict a single dependent variable (Y) (Original Definition). By noting that you will get two equations for two dependent variables.
in SPSS, you can do multiple regression from A,B->C and A,B->D.
This is the calculation technique. But if you want to test or run this model together than you must use PLS-SEM or CB-SEM. For PLS-SEM you can use smartPLS software, for CB-SEM , you can use AMOS.
Or you can do 2nd order , by merging C and D together. Then C and D will become E and you can test A,B->E
Usually , we do not put any equation because of the standard error. We just test the positive or negative relationship, its significance, Variance (R square) and effect size (f sqaure) .
Check the attached paper for multiple dependent variables and multiple regression.