if in regression models homogeneity is violated, the variance can in principle depend on both: Predictor and outcome variable(s).

In case of a dependency on categorical or continuous predictor variables, there are many ways to model different dependencies, e.g. using GLS models.

In contrast, regarding a dependency of the variance on the outcome, I only know Poisson regression where the variance equals the expected value and thus increases with the outcome. But if I have another dependency of the outcome (e.g. variance = outcome^2), does somebody know ways to model this?

Thanks