Insure rentals using same company as primary residence?

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I have an existing policy/umbrella on my primary residence with State Farm.  I'm looking to add 3 new out-of-state rentals.  Should I got with State Farm?  Or, can I go with any insurance carrier with the best rate/coverage.  I heard that when dealing with two different insurance companies, one company will often tell you to work it out with the other.  i.e. my personal residence umbrella won't cover the rentals because they're with another company.