Hi @auth0rocks !
It would not be possible to use a combination of Identifier first along with Identifier + Password within the same tenant, since its a tenant level configuration.
If you wanted to continue to use New Universal Login, you could look to achieve this UX by having two Auth0 Tenants, one configured for DBs connections and the other for SSO and Identifier First. Although you wouldn’t be able to have a button on the Auth0 prompt to take the user to the alternative login prompt, you could look to add your own button/text and logic by Customising the Page Template. See examples such as the page footer with links etc. for ideas.
Hope this helps!