I assume you mean the EIN of your LLC (?) if so I don't see why not. Any dealings of the LLC (including bank accounts) it's member K-1s, etc should be done under it's own EIN. Otherwise the corporate veil is viewed more transparent, if not pierced by some litigations. Additionally with an added member (or whatever entity type) it's no longer a sole member LLC which is good. Since sole member LLCs have not been treated (in a court of law suit) as a
separate entity with as much regularity as multi-member LLCs. However the bank may also want the SS number of the tax matters partner of your LLC (namely you).