Social Security Questions? Ask a Social Security Expert
Normally the answer is no. You cannot collect SSA benefits and SSDI at the same time.
There is an exception and that depends on your age. If you took early retirement through Social Security, which is possible at 62, before being approved for disability benefits then you could apply for SSDI. If your disability started before you started taking regular SSA benefits then SSA may pay you the difference.
Getting VA and SSDI is not prohibited.