“come in” (like answering a door knock)

Not really for that. You would use 进来, 请进, or just 来/来来 in casual speech. The 来 derivative handles the invitation.

进去 marks movement into a space away from the speaker. It is for actual entry, not invitation. Eg:

胡同太窄, 救护车开不进去

(Hútòng tài zhǎi, jiùhùchē kāi bù jìnqu.)

The lane is too narrow for the ambulance to drive in.