Yes, you may be able to purchase and own more than one life insurance policy.
In fact, many people have life insurance through their employer, and own more than one individual life insurance policy on their own, outside of the employer provided coverage.
It depends on your life insurance needs, if you are insurable, if you can afford the coverage, and if you are approved by the insurance companies for the additional coverage.
When you apply for life insurance, their is a question on the application about whether you own any life insurance already, and if so, how much life insurance and how many other policies.
The insurance company asks these questions to make sure you aren;t getting over-insured, so there isn't a risk of suicide in the future, since life insurance policies have a 2 year exclusion (one year in some states) for suicide.
However, most insurance companies will allow you to have up to 10-20 times (total) your annual income in life insurance. This means if you earn $100,000 per year, you may be able to buy up to $2,000,000 of total life insurance among all of your life insurance policies.
Here's an article that provides more information on the question - Can you own multiple life insurance policies?