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Yes, sole proprietor taxation is a flow through straight to your own income tax return. You really didn't need a separate EIN -- only your social.
S-corp is also a flow through income tax taxation method but has some differences. As such, you should obtain a separate EIN. And since it is a separate entity, you do need a separate EIN, even though income will go on your personal return.
Because of this, and because you will want to maintain the limited liability protection conferred by a corporation, you should open a new account in the name of the corporation.
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