I think what you want to know if whether your candidature looks stronger with multiple referrals or not? Isn't it?
Honestly, the value of the referral is 'familarity' component. When someone refers a candidate, it means that person indirectly tells the recruiter that 'I know this candidate would be a good fit for the company'.
Now, if more employees say that about you, of course it adds more confidence in your candidature. Similarly, more the seniority of the referring consultant, more is the confidnece in your candidate.
But please understand that, in the recruitment system, the person from whom the referral came first gets registered as your referring partner. More senior that person is, better it is for you.
To give myself best chance, when I know multiple people in the firm, I will do this:
1. Tell the seniormost among them to refer me
2. Use names of other/s in my other communication like cover letter etc. to let the recruiter know that a lot of people know me in your firm, so give me a chance to inteview with your firm!
Hope this helps,