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Can NonlinearModelFit consider the error parameters dependent ?

Dear All,
I am using NonlinearModelFit to fit data with a function with 4 parameters.
With Marquardt Levenberg Algorithm the errors are considered independent, but in reality errors are dependent each other.
Is there a build in function which  I can use that when I type
nonlimearmodelfit["ParameterErrors"] I can obtain an evaluation of the errors that takes into consideration that they are dependent each other?

Many thanks,

Best regards,
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