How many change of goals can a story take?

This depends completely on what their underlying fears and dreams are. If they fear being lost without the antagonist, therefore their goals always match whatever the antagonist wants, then I doubt the reader will question that. (Though they might question why the antagonists goals are changing so often.) If their dreams are to have a loving family and this antagonist is a part of it then it makes sense to change the goals to achieve the dream. Again a reader might question the antagonist more than the protagonist.

Within the text itself ‘hanging a lantern on it’ might be a good way to dismiss reader worry about the change in goals.

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