The simple answer is yes, you can have your own insurance and be on your parents' insurance at the same time. However, it's important to understand that there may be certain factors influencing this situation.
First off, there are certain rules and restrictions around having multiple insurance policies. Most insurance companies will not allow you to double, or "stack," coverage, meaning they won't provide duplicate coverage for the same thing. For example, if your parents already have a medical insurance policy, they won't provide you with one as well.
It's also important to understand that if you and your parents have different insurance policies, there could be a conflict of interests in certain situations. For example, if both you and your parents are injured in a car accident and you file claims to both insurance policies, the companies may try to deny coverage.
Finally, you need to make sure that your parents' insurance policy will cover you if you're under a certain age. Most policies will only cover you until you're 26, but it's best to check with your parents' insurance company to make sure.
If you have any further questions about having your own insurance and being on your parents' policy at the same time, it's best to speak to an insurance expert. An insurance broker can provide you with more detailed information about the rules and regulations that apply to you and your parents' situation.