Currently, there is no support for **fit_params in the fit method of _BaseStacking:

As introduced in issue #15953 for _MultiOutputEstimator, it seems natural to extend the utility to stacking. A proposed implementation in the base stacking class is as follows:

from ..utils.validation import _check_fit_params

def fit(self, X, y, sample_weight=None, **fit_params):
    # Right before predictions = Parallel...
    if fit_params:
        fit_params = _check_fit_params(X, fit_params)
    else:
        fit_params = (dict(sample_weight=sample_weight)
                      if sample_weight is not None
                      else None)
    # Then, utilize fit_params in the parallelized cross_val_predict

Subsequently, alter the fit methods for StackingClassifier and StackingRegressor such that they support **fit_params. If this is favorable, then I can write an implementation and start the pull request.