Yes, you can buy multiple life insurance policies.

When you apply for a life insurance policy the application will ask if you own other life insurance, if so, how many life insurance policies and how much total life insurance coverage do you already own?

The insurance company asks to determine if you are over-insured.

They don't want there to be an incentive for you to take your own life in the future. However, life insurance policies usually have a suicide exclusion of 1 or 20 years, depending on the state you live in - life insurance is regulated by the states.

Most life insurance companies will allow you to buy up to 10 to 20 times your annual income in life insurance coverage.

So, if you make $50,000 per year, you may be able to buy up to $500,000 to $1,000,000 of life insurance coverage.

Here's an article with more information explaining how many life insurance policies can you have?