Can you receive private disability payments and also receive social security disability payments?

The broad answer to the question is Yes. However, whether both categories of benefits are payable in a particular situation will depend upon whether the applicant is found to be "totally disabled" under SSDI guidelines, and how the private disability policy defines disability.

A very comprehensive explanation of the Social Security disability process appears on the Social Security website maintained by the Social Security Administration. Much, if not all of the initial application process can be done online, or you can go to a local Social Security Office. It often takes a while to get a determination, so patience is a virtue. The most critical element of the process involves medical documentation of your inability to work.

A private disability insurance policy will define that which constitutes disability, and that definition must be met for benefits to be triggered. There are various definitions and the precise wording will dictate your entitlement to benefits (such as, you may be able to collect if you are disabled from doing that line of work that you did at the time of the disabling event, or you may be able to collect only if you are unable to do any sort of work).

The long and the short of it is that you may very well be able to collectboth, but the specific answer is fact-driven.