Can I qualify for both SSI and SSDI?

It is possible to qualify for both SSI and SSDI, although it is unlikely. If you qualify for both forms of benefits, that is called concurrent benefits. Unfortunately SSI stands for Supplemental Security Income and will only apply if your income is low enough to be supplemented. In other words, you would only get SSI if your SSDI benefits are too low. At that point, SSI would step in and supplement your benefits to bring them up to a combined total of $710 a month.