Yes. My daughter collects both. If your SSDI is more than the amount you would get from SSI, then you would not collect both, but my daughter gets less than the amount from SSDI and SSI makes up the rest. Therefore there is no extra money available. Well, that might not be quite true. I think they let you keep $20 per month from another source, which in this case is SSDI. The only real advantage is that with SSDI, you can get Medicare after a two year waiting period (at least in my state), while with SSI only you qualify only for SSI.