Impact of multiple deals on credit score

[Kirsten Milliken]

I am in the process of doing a cash-out on a rental property while also looking to buy a new home.  Last month I refinanced my primary residence.  Before I submit applications and give permission to pull my credit score, I want some insight into how having my credit pulled multiple times is going to impact my score.  

Should I have each one pull it at the same time? Wait? Have the most important one pull it first? Or can banks share a credit report?