How to add dependency within the randomness of an outcomes between records

For simpliness, I will talk about Generalize linear model (GLM) as an example.

The GLM assumes the randomness of an outcome to be independent (all error terms are iid). Let imagine that the actual outcome (Y) is the losses.

Which techniques can I use to incorporate dependency within the randomness of the outcome between each record Y(i) (where Y is the outcome losses and i is one row of a dataset representing a physical building), without loosing alot of interpretability within the proposed solution (I don't want my solution to be a black box for a non statistician). For example, I want to incorporate the dependency that some records share together, because their building are geographically close together (ex: the randomness within the losses caused by an hurricane that hit this area will be share by multiple recorda at the same time, therefore, there will be dependency within the randomness of the outcomes and a GLM will not catch this without any adjustment).

Thanks,