Rookie networking question

Hi all,

I'm fresh out of an MBA and actively looking for jobs in Product Management. I'm reaching out to potential peers on LinkedIn with a simple message that states that I'm interested in their company and want to learn more.

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In the past couple of weeks, I've had extremely insightful conversations that have helped me tailor my resume to match the job and also some referrals. In general, I enjoy talking to people and learning more.

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My problem is that a lot of people are merely accepting my request and not responding to my prompt. Should I send a follow-up message or is that too pushy? If yes, what could I send?

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