Homeowners insurance is written for one homeowner and one home. Just as you do not insure multiple homes on the same insurance policy, you would not purchase more than one policy for a single home. Aside from driving up the cost of your home insurance by double or more, having duplicate policies would also create legal confusion if you were to file a claim on the property.
Even if you had multiple home insurance policies in effect, you would not be able to get coverage from all of them, and getting any of them to settle could become a chore. Having two homeowners insurance policies at the same time would give the insurance companies a legal loophole whereby each company could say that the responsibility for the claim rests with the other company. And if you tried to file a single claim with both companies, you could not only lose both policies, but be charged with insurance fraud as well, a very serious crime.
If you have two homes, each one would be insured separately. In this case, you would have as many homeowners' policies as you have homes. Keep in mind that there other insurance options available to reduce costs, such as declaring one home a vacation home. Additionally, if you are renting any of the homes, your home insurance for that property would be reduced to landlord insurance which does not cover liability for the inhabitants or their personal property.
Even though you cannot combine home insurance policies into a single policy, you can still save money by purchasing all of your home policies from a single insurance company. Most companies offer discounts to people who have more than one insurance policy with them, whether all of the policies are for home insurance or for a variety of coverage needs.