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Say I have an imputation model with two response variabiables (R1 and R2) and four explanatory variables (E1, E2, Cons, School). This is a two level model with everything nested under school. Say I estimate my missing data conduct my analysis and then a reviewer suggests another variable with missing data (R3) should be included. I would have to re-estimate all of my data (R1-R3) rather than R3 alone beacuase this is a joint model, correct?

That's correct you will need to re-impute
Harvey Goldstein