Accessing regression coefficients when using MultiOutputRegressor

I am working on a multioutput (nr. targets: 2) regression task. The original data has a huge dimensionality (p>>n, i.e. there are far more predictors than observations), hence for the baseline models I chose to experiment with Lasso regression, wrapped in sklearn's MultiOutputRegressor. After optimizing the hyperparameters of the Lasso baseline, I wanted to look into model explainability by retrieving the coef_ of the wrapped Lasso regression model(s), but this doesn't seem to be possible. I'm now wondering how I could look into the model's coefficients and have a better understanding of the predictions it makes.

My idea was to return the estimator with the best hyperparameters from GridSearchCV by setting refit=True. Then, accessing the estimator argument of it which yields MultiOutputRegressor(Lasso()), as intended. Now MultiOutputRegressor also has an estimator argument, accessing it would return Lasso(). Last, Lasso has a coef_ argument that returns the coefficients of the regressor. According to sklearn documentation the shape of the array returned by this coef_ argument is either (n_features,) or (n_targets, n_features), so multioutput regression coefficients seem to be supported.

Sample data and code:

from numpy import logspace
from sklearn.datasets import make_regression
from sklearn.model_selection import GridSearchCV
from sklearn.multioutput import MultiOutputRegressor
from sklearn.linear_model import Lasso

X, y = make_regression(n_samples=1000, n_features=10, n_informative=5, n_targets=2, random_state=1, noise=0.5)

search = GridSearchCV(
MultiOutputRegressor(Lasso()),
param_grid={'estimator__alpha': logspace(-1,1,3)},
scoring='neg_mean_squared_error',
cv=10,
n_jobs=-1,
refit=True
)

best_model = search.fit(X, y)

print(best_model)

print(best_model.estimator.estimator.coef_)