After leaving my job, I continued my insurance under the Cobra coverage. Is it possible to extend the coverage past the initial 18 months?

You can convert to a private pay policy if the carrier has a conversion option after COBRA is exhausted.

If you are disabled within the first 18 months of COBRA there is the 11-month extension.

Regarding the 11 month extension if you are disabled -- there are certain criteria that an individual must meet in order to have COBRA extended. 1) you must have been determined by the Social Security Administration to have been disabled either at the time you first became eligible for COBRA or within the first sixty days after the termination of your active plan coverage. Although the SSA can make the determination that you are disabled at any time during the initial 18 months of COBRA coverage, the disability must have begun or existed before the end of the first 60 days of COBRA. 2) The disabled person must supply a copy of the SSA determination letter to the COBRA administrator within 60 days of receiving it and before the end of their initial 18 months of COBRA.

Individual who are first disabled more than 60 days after the beginning of their COBRA coverage are not eligible to extend the coverage.