I have finally found my answer from Alan Belkin:
The passage starts from 3:12. There Mr. Belkin details how to gradually change the key by sneaking and notes from the new modal key.
I have one more thing to add, that in his example 8, it helps a lot that the new key's notes are introduced in a new phrase, in a new "musical thought", if it makes sense, so the wandering from one key to the other does not sound surprising.