BIGIP how to handle multiple IDP each with multiple external SP

Here are a couple of tools that I often use for SAML configs, to help you decode the information that goes between the SP and the IdP;

• https://www.samltool.com/online_tools.php
• SAML tracer (browser plugin, available for Firefox and Chrome at least)

I'd start with the SAML tracer, run it once in your browser while you go through the login process, and see the SAML messages from SP to IdP, and back again, and dissect them from there to find the information you need.

It's indeed often a puzzle to see how everything fits together and can take some time to set it up, but as long as you like puzzles, you should be fine... ;)