You’ll become eligible for cheaper free insurance quotes if you get all your policies from the same insurance company. This is known as a multi-policy discount and is available with all insurers. But you could make more savings with different insurers than you’ll make from a multi-policy discount. This might not always be the case for everybody depending on how well you shopped before purchasing.
However, you will do well to check first. Take your time to get and compare as many homeowners insurance quotes from as many quotes sites as possible. You will almost always save much more if you obtain and compare quotes from not less than 5 insurance quotes sites because you will be less likely to miss many great offers.
But if you don’t want to go through all such hassles, take what discount you’re offered. After all, half a bread is better than none.