Two-way MANOVA - Total Effect of Independent Variables on Response Variables Together

I have run a two-way MANOVA in SPSS. In the model, there are two fixed (independent) variables A and B, and two response (dependent) variables X and Y.

I am trying to ascertain the total effect of A and B on X and Y, i.e. A's effect on X and Y, plus B's effect on X and Y, plus A*B's interaction effect on X and Y.

The "Multivariate Tests" results in the SPSS output only show the effect size statistic Partial Eta Squared by factor (A, B, and A * B), which unlike Eta Squared, is not additive and does not allow me to add the factors' effects together.

I then looked at the "Tests of Between-Subjects Effects" table, which shows Type III Sum of Squares by factor (A, B, and A*B) and by response (X, Y), which allows me to calculate the sum of the effects (Eta Squared) of A, B, and A * B by response (X, Y), but does not allow me to calculate the total effect on X and Y together (i.e. on X and Y's linear combination).

(I tried to run similar commands in SAS and have got the same problem.)

(The reason I cannot use canonical correlation analysis is that I have other independent variables in the overall conceptual model which are categorical/nominal in nature.)

Is there any way I can calculate such a total effect of the independent variables on the response variable together?

Any thoughts would be highly appreciated!!!