Multiple K8s Certificates via TLSStore(s)

I'm attempting to use multiple certs with Traefik 2.2 One cert is from lets-encrypt via cert manager, one is from a different CA manually tossed in there. This is what I tried.

apiVersion: traefik.containo.us/v1alpha1
kind: TLSStore
metadata:
  name: default
  namespace: default
spec:
  defaultCertificate:
    secretName: wildcard--first-certificate # from cert-manager
---
apiVersion: traefik.containo.us/v1alpha1
kind: TLSStore
metadata:
  name: default
  namespace: default
spec:
  defaultCertificate:
    secretName: wildcard-second-certificate # from other CA

I have also changed the second store's name from default to something else because, but the docs for TOML versions indicate that will be ignored.

Either way it doesn't work. It only ever uses one cert. Shouldn't it know with SNI which to use, or is it only ever loading one? Logs don't seem to tell the story. I could be missing something.

Is my approach totally off, or do I have something wrong here?