Is there any option to pass any other variable value (apart from User Name & Password) from external logon screen to my.policy?

This white paper discussing RSA OTP integration is doing the same thing that you're asking about. It's creating an additional variable in that external login screen that can be used in the policy. Take a look at the screenshots:

https://support.f5.com/kb/en-us/products/big-ip_apm/manuals/product/apm-authentication-single-sign-on-11-5-0/6.html

In addition to the login page and the above method to create custom variables, you can use the variable assign agent in the VPE to create anything under the sun. This gentlemen rocked it with this article explaining different use case examples of the feature:

https://devcentral.f5.com/codeshare/apm-variable-assign-examples-1107