Can I apply L2 EAD and simultaneously apply for L1A Blanket/Individual ?

My husband got his L1B stamping done and alognwith I got my L2 Stamping done. I visited US with him to help him settle down for couple of weeks and at the same time applied for my L2-EAD. I have received the receipt of the same and approval is under progress.

I am currently employed with India based services organization. On my return , my employers told me that they wil be processing my L1A individual/Blanket (My L1A Blanket was rejected more than year back ) as they are mapping me to an onsite role.

I needed to understand whether it is fine to go ahead with my L1A Blanket/Individual process while my EAD is under progress.

Does someone has a similar experience ?

Moreover, Should I again apply for L1A blanket or apply only individual ?