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response correlated among groups

Dear list members

I would like to fit a model relating a gaussian response variable y to some continuous predictor variables (p1 and p2). 
The response is correlated among the classes of a factor (p3).

Is it possible to set up a mixed model that accounts for the correlations among classes of p3 in the response?

I would appreciate help on how to code such a model, if possible.

Many thanks in advance,
Rafael