Good afternoon (morning in CA)Customerand welcome back.
Yes you can receive SDI and SSID benefits at the same time, however your SSI disability benefits could possibly be reduced based on how much you receive from the SDI benefits. Here is a little more information on this directly from the following website: http://www.disabilitybenefits101.org/ca/programs/income_support/ss_disability/ssdi/faqs.htm#_q361
Please let me know if I can be of any further assistance and thank you for the trust you have placed in me to answer your questions for you. If you need any more information or more clarification, please do not hesitate to ask. I look forward to talking with you again very soon.