Answer: During open enrollment, you can sign up for a Marketplace plan even if you already have COBRA. You will have to drop your COBRA coverage effective by the date your new Marketplace plan coverage begins. After open enrollment ends, however, if you voluntarily drop your COBRA coverage or stop paying premiums, you will not be eligible for a special enrollment opportunity unless you exhaust your COBRA benefits or if you lose government subsidies or employer contributions to your COBRA premium. (45 C.F.R. § 155.420; https://www.healthcare.gov/unemployed/cobra-coverage/).
On Private Health Insurance Coverage & The Health Insurance Marketplace