What’s the polite and strategic way to ask for referrals from multiple people in the same team?

I’m applying to a specific team and have networked with a few people in it. How should I approach referrals without overstepping? Should I ask multiple people, or could that backfire?

Here’s my situation:

• A contact (D+) has already forwarded my resume to the hiring team but didn’t share any advice or feedback when he responded, was annoying direct.
• I also know an associate I’ve spoken to briefly. I’m considering reaching out to them to discuss the role and get insights—not to ask them to forward my resume.
• Lastly, I know a VP in the team who I’m thinking about asking to forward my resume as well.

My concern is that this might seem excessive or hurt my chances if these people talk to each other. I also don’t want to come across as pushy or overbearing. That said, since my resume has already been forwarded once before with no outcome, I’m wondering if it’s worth trying to leverage other connections to increase my chances.

What’s the best way to handle this respectfully while being strategic and not burning bridges or annoying people because this is a somewhat small/specific team and do you tell them you spoke/reached out to the other person?

P.S. I would also be curious to hear how the teams track applicants internally? When you have multiple VPs and MDs, etc., do they all direct resumes to a single person who runs it? I have heard that for some teams keep spreadsheets tracking people they have spoken with and active pipeline. Is there any point to reaching out to the HR lead?