DESeq2 contrasts multiple treatments two genoptypes

Hi

I have an experiment with three treatments (E,U and control (C)) and 2 genotypes (1 and 2).
I have 3-4 reps for each conditions and each genotype.

I know how to do the comparison (E-C vs U-C) for each genotype separately (with "design = ~ treament" and treatment column containing E, C or U). And then I look at the overlap/no overlap between both DEG lists (DEGs E1vsU1 and DEGs E2vsU2).

However, I think there is a better (statiscal) way would to analyze E vs U changes depending on genotype.
In other words, I would like to do the following comparison:

(E1-C1/U1-C1) vs (E2-C2/U2-C2)

which should yield me those genes in the EvsU comparison for genotype 1 that are differentially expressed compared to EvsU comparison for genotype 2.

Thank you in advance.