As a Illinois notary can I notarize a process server's affidavits from Indiana?

From what I'm reading, yes, but you have to attach a Certificate of Notarial Authority.

You mean can you notarize the server's signature, right?

You are in Illinois ? You can not be out of state and do it. You are just witness a signing, as long as you are in your state, you may

I can notarize for another State in NY BUT I have to attach a certificate, not just use my stamp and seal.