Yes, you may own one of more term life insurance policies depending on your own specific situation and life insurance needs.
For example, you may own one 30 year term life policy to protect the mortgage on your home, and own a separate 25 year term life policy to make sure your kids have money for college should you die unexpectedly.
By owning several term life policies you can get the coverage you need for your specific insurance needs, and pay the lowest amount overall, because you are designing a life insurance plan based on your needs, with each term policy serving a specific purpose.
Here's how to buy a term life insurance policy.