Can you receive disability from your job and disability from social security at the same time?

Yes, it is very common for disability insurance plans to include a clause for social security disability, meaning the insurance company will pay a portion of the monthly benefit, expecting that you would apply for social security benefits to pay for the "Supplemental Social Security benefits". In the event you get declined by Social Security, then the insurance company would cover the additional supplemental benefits.

Employer group plans as well as individual disability insurance plans can include that clause.