Q: Why would a Cobra insurer request info about whether or not I, my spouse, and/or dependents had coverage under another health plan since the date Cobra coverage started? (which was several months ago and all premiums have been paid.). If I did, how would that affect anything, and why? A: If you have other health insurance that doesn’t exclude pre-existing conditions you are no longer eligible for COBRA. You can not have COBRA and other insurance at the same time. Your insurer (insurance company) through COBRA continuation has the right to inquire about other insurance.