KeePass is a software, not a service, so it doesn't really authenticate you. It uses a key to decrypt database, and that key derivation could be based upon various sources, including 2FA-like setups.

There are various plugins for multi-factor key derivation existing for at least several years already. You just have to chose one that suits you depending on what your second factor is (PKCS#11 token with RSA key, OATH HOTP generator, Bluetooth-based key storage, etc). Platform support may vary, though (so, not sure all options are supported, say, on Android).

You can use a key file in addition to password, so yes.

So not just proprietary software, but saas using a proprietary client? In for a penny, in for a pound I guess.

1Password and KeyPass don't even do "one factor authentication". This is because you are not authenticating to any service as all. Your Master Passwords for these are "encryption" passwords not "authentication passwords".

Authentication is about proving your identity to a system that has the power to grant you access to something. They can have you go through multiple steps. But with 1Password and KeyPass, you already have full access to your data (it is on your disk). Your password is used not to prove your identity, but instead it is used to derive a key which can decrypt the data that you already have access to.

Services that you need to authenticate against face different sorts of threats than those which are based solely on encryption. An authentication system protecting high value data simultaneously make multi factor authentication possible and necessary. For encryption based systems, MFA literally makes no sense.