Should I still require 3x rent for a property that is $5000+ a month?

[Alma Mills]

We have a beautiful 5 bedroom 3 bath that we are going to be renting for $5500 a month and are considering lowering the income requirement.  Normally we usually require income of 3x the rent or at the least rents being 40% of the income.  Our thought process is that a family should be able to easily live on much less than $11,000 a month after housing is paid for.  

We are in Los Angeles 2 block from Culver City if you were wondering.  

What are you thoughts? anyone tried doing the same and found it worked or discovered problems?