Yes. In fact, you may own more than one term life policy and more than one permanent life insurance policy.
It depends on your personal life insurance needs, your situation, your budget, and how much life insurance you already own.
The insurance company doesn't care how many policies you have, but rather how much total life insurance you are insured for.
Why? Because, if you are over-insured, it may give rise to a potential risk of suicide in the future, if you are worth so much more dead than alive.
Yes, life insurance policies may pay out a claim for suicide, if it occurs more than 2 years after the start of your life insurance policy (one year in someone states).
Learn more about buying multiple term life insurance policies.