Thank you in advance for any technical advice you can give.

I am currently using MICE to address missingness for a dataset, wherein I am conducting logistic, ordinal, and Cox regressions and am clustering use vce (Cluster, VarName). I'm using mi register wide for the ordinal/logistic and then mi register long for the Cox regressions. I've been asked to assess the interactive effects of two ordinal 3-category variables that are being imputed. I believe this means I should re-do my imputation model, to incorporate the interaction term, and then conduct the regressions. If the omnibus product term is significant, I can then show stratified analyses by one of the imputed variables. I think I'm supposed to use the "by ()" command in maybe the specification for the other imputed variable (and then not use by () command for the imputed variable that's the stratifying one), but wanted to make sure I'm on the right page. Any appraisal support would be great.

If it helps, this is the situation with variable names:
Imputed variables: residential instability (1, 2, >=3 residences); neighborhood disadvantage (low, medium, high; by(Block Group))
Interaction: residential instability*neighborhood disadvantage
If sig, I plan to stratify relationships of residential instability to outcomes by neighborhood disadvantage.

Thanks so much!
Yami