Optimizing the fine-tuning of PCA / KernelPCA n_components

This example shows a way to use cross-validation to select the best value for n_components in the PCA:
https://scikit-learn.org/stable/tutorial/statistical_inference/putting_together.html

However, it seems that there would be a more computation-efficient way to do it, fitting the PCA only once with the maximum value of n_components tested, and then applying the transformation with different values of n_components.
Indeed, when using GridSearchCV to optimize n_components in the PCA, there is a new fit for each iteration.
As the PCA can be very slow, optimizing it would be cool.

Any idea on how to do it easily with current implementation of PCA and GridSearchCV ?

Start with the linked scikit-learn cross-validation tutorial and compare how PCA and KernelPCA interact with GridSearchCV when n_components varies. Determine whether fitting once at the maximum value can be supported without changing expected estimator behavior; done requires an agreed design and evidence that the optimization preserves correct cross-validation results.