APM Sharepoint

We are attempting to migrate a Sharepoint Site that has 2 virtual servers from a Netscaler to F5. There are 3 separate user authentication domains. When I test directly to the Sharepoint site, I can successfully log in w/o domain notation.

Is it possible to setup a F5 Logon Page that does not authenticate the user but only collects the username and password and passes to it the Sharepoint server?

do you have APM module installed? If your users are using domain joined machine and they use domain credentials to logon you can take a look at the option of Kerberos SSO.