A few options if you want to maintain MFA:

For my Okta account, they support push notification to their app on my phone as an alternative authentication measure.

Another approach is a bluetooth (or NFC) enabled device (like your phone) that actually caries the private key. When using a borrowed computer, the signed attestation data is shared with the borrowed system, but that can only be used once, since the private key is never transmitted.

So basically you can either have a side-channel to another MFA method, or a relay where you don't need to trust the intermediary beyond the current session.