Do I need a separate EIN for my sole proprietor business if I have an EIN as a household employer?

Hello. I am a household employer with an EIN to report taxes on my Schedule H. If I start a new business as a sole proprietor, do I need a new EIN?

IRS publications confirms the reverse, where a sole proprietor can use an exiting EIN for household employees. I can't seem to find info for my situation.

Thanks!