If you feel that your health insurance sum insured is not enough, you can in fact, have it increased. However, you have to make sure you do it before the policy begins. If the policy period has started, then you have to wait for it to end. Only after that, you can get the health insurance sum insured increased during the renewal process. However, no one stops you from having two health insurance plans at one time. Hence, if you think that your cover is not enough, you can purchase a second health insurance plan to cover the difference.