going beyond the F5 provided SAML AuthnRequest

Generally speaking, the configurable options are (only currently I hope) limited to what you can set in the profiles. That said, if 1) depending I suppose on the the optional fields you're considering, and 2) you don't care about signing or encrypting the AuthnRequest, you could layer the SP policy behind a VIP and iRule to tweak the outgoing request however you wanted.

Definitely doable.