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Yes, you can receive Social Security Disability Insurance (SSDI) and Supplemental Security Income (SSI) at the same time. Social Security uses the term “concurrent” when you qualify for both disability benefits it administers.
However, drawing SSDI benefits can reduce your SSI payment, or make you ineligible for one. That's due to differences in the programs’ intent and eligibility criteria.
Both SSDI and SSI provide benefits to people who meet Social Security's definition of a disability: a physical or mental health condition severe enough to prevent you from doing most work for at least a year. But SSDI provides payments to disabled people regardless of their financial situation. Qualification is tied to how long you were employed in work for which you paid Social Security taxes, and payment amounts are based on your average lifetime earnings.

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SSI, on the other hand, is needs-based. It pays benefits to people who are disabled, blind or at least 65 years old and have low incomes and limited financial resources. It is unrelated to your employment history; you can receive SSI even if you never worked or paid Social Security taxes.
But you can't get SSI if what Social Security calls your “countable” income exceeds a federally set threshold, which in 2023 is $914 a month for individuals and $1,371 for couples. Those figures are also the maximum federal SSI payments.
Social Security considers SSDI and other benefit payments to be countable but exempts $20 a month from that tally. Thus, if you get an SSDI benefit that exceeds $934, you don't qualify for SSI. If your SSDI payment is less than that, you may be able to get SSI, but it will be reduced by most of the amount of your SSDI.
For example, suppose you qualify for SSI and for an SSDI benefit of $500. With the $20 exemption, Social Security will reduce your SSI by $480. You'd still get $500 a month in SSDI and $434 ($914 minus $480) in SSI.