"in the way of X" is an idiomatic expression meaning "in the style or form of X" or "like X". "without much in the way of grandiose expectations" therefore means "without much in the style/form of grandiose expectations". In effect, it may be little more than a fancier way of saying "without any/many grandiose expectations".
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marxman1968Thank you for your reply! I would like to ask you a question in a private message. Is that OK?On the whole I try to discourage questions in private messages. However, if it is a language question that is very important for you, and you cannot post it publicly for reasons of privacy, then yes. I only answer questions about individual language point