SSL offloading in F5 with 2 wild card certificate on same VS

You would need to create 3 clientssl profiles: 2 for each of your wildcard certificates and a default profile to cover the rest of cases, this is by design.

On the clientssl profiles for the wildcards you need to configure the server name setting which supports wildcards. More here: https://support.f5.com/csp/article/K14783

Then you add the 3 clientssl profiles on your virtual server. If you are doing ssl offlocad then you don't need a serverssl profile, you need to have to pool members configured on port 80/http. You may need to add an HTTP profile to rewrite redirects in case your servers send those using http instead of https ( in the HTTP profile there is the setting redirect rewrite, I use most of the times the all option)