Premier Health Insurance Agency Claimed

Yes! You can enroll with a private health insurance carrier outside of open enrollment. These companies offer excellent coverage, large networks and flexible coverage options.
These are sometimes called "off-market" plans since they are not offer through the government exchanges created under the Affordable Care Act.
Also, they are purchased directly from the insurance company with the help of a licensed health insurance agent. You may hear these plans referred to as "individual" plans. This does not mean that only one person may enroll on them, it means they are not a "group plan" which are structured very differently and offer through employers.
So if you are looking to switch plans or get a new plan outside of open enrollment you may want to search for insurance using those terms.

Typically private health insurance is more affordable than group plan, especially when it is medically underwritten and join a "low risk pool" of other isured individuals and families.
If you are leaving coverage from an employer where you received health insurance as a benefit, your cost to purchase private health insurance may appear to be more expensive.
However, if you were to pay the full price of the group coverage offer through your job you would see the real cost of the insurance. This is why many people say that the COBRA is so expensive. This is the full premium that you must pay in order to keep the same benefits from your old job.
It's not that COBRA is expensive, it's that your group plan was expensive and your employer was covering a large portion of your monthly premium payments.