Feature request

Do you want to add more fields to the login form? Or do you want to do extra validation to the current login form?

If you only want to do extra validation of username or password, you could create a custom ‘authenticate’ filter then do your extra validation.

Extra validation only

Can you expand on how/where to create the custom filter please

I just realized you are talking about registration or signup, not login-form.php. Registration/signup template is register-form.php. TML author has a page which describes how to add custom registration fields – https://www.jfarthing.com/development/theme-my-login/adding-extra-registration-fields/

Note that only works for regular WP and not WP multisite. WP multisite uses different filters/actions.