Create a soft label classifier from any scikit-learn regressor object

softie.py

from sklearn.base import BaseEstimator, ClassifierMixin
from scipy.special import expit, logit


class SoftLabelClassifier(BaseEstimator, ClassifierMixin):
    def __init__(self, regressor, eps=0.001):
        self.regressor = regressor
        self.eps = eps

    def fit(self, X, y=None):
        y = np.array(y)
        # 1 or 0 will give us inf of -inf
        y[y == 1.0] = 1 - self.eps
        y[y == 0.0] = self.eps
        y_logit = logit(y)
        self.regressor.fit(X, y_logit)

    def predict(self, X, y=None):
        preds_regression = self.regressor.predict(X)
        preds = expit(preds_regression) > 0.5
        return preds

    def predict_proba(self, X, y=None):
        preds_regression = self.regressor.predict(X)
        preds = expit(preds_regression)
        return preds

If I had a multi-class problem (≥3 classes), how would I proceed?