Usually one solid referral is enough. Chasing a second or third referral just for the sake of stacking them often creates more noise than benefit.

What matters more is the credibility of the relationship and whether the person can genuinely vouch for you. A weaker senior referral is not automatically better than a stronger referral from someone who actually knows you.

So focus on quality and fit rather than trying to optimize the title of the referrer. You may also find it helpful to read what makes a strong consulting referral if you want a more structured way to practice this.

I would rather have one real referral than three random ones.

Seniority matters less than people think if the person barely knows you.