Cognito - Auth0 SAML request

Hi, I'm using Auth0 as SAML identity provider in conjunction with its Organization feature. I have multiple clients in Cognito and for each client I'd like to pass a different organization query parameter in the login URL. The login URL is in the SAML metadata. So I need to modify it before it's sent out to Auth0.

eg: <SingleSignOnService Binding="urn:oasis:names:tc:SAML:2.0:bindings:HTTP-POST" Location="https://<Auth0-domain>/samlp/<Client_id>?organization=<organization_id>"/>

I'm wondering if it's possible to intercept the request before it goes to Auth0 through a lambda trigger? Or perhaps any other methods?

Please advise, Thanks!