Force Authy usage on signup and next login for existing users?

We love what Authy has to offer and would like to incorporate into our system. We have a nuanced approach for integration that I would like to describe :
We would like to force Authy MFA on signup and next login for existing users. We would like a one time MFA, as well as MFA on password reset.
For users that do not have a cell phone listed in their profile, we would like to force them to provide one from the front end.
Is this possible in whole or in part?

https://wordpress.org/plugins/authy-two-factor-authentication/