A second password would not be 2FA, it would just be two passwords.

2 Factor refers to 2 different ways of proving your identity. Something you know (your password) and something you have (your phone). You can also get dedicated 2FA devices, they look like a little USB drive with a screen, but honestly, they are more of a pain to deal with than your phone, and most 2FA systems do not have support for all the different brands and devices.