Are you talking about H4/EAD or TPS/EAD in H4? Either way, you can apply for both EAD and SSN. All you got to do to get SSN is to go to the Social Security Office with your passport and EAD card. They will send out your SSN in about two weeks.

I also read the news that now onwards they are approving both EAD and SSN in a single form for certain Visa types. I am not pretty sure about it. You can check that on USCIS website.