By template, the availability of refinement is restricted. By power, only channeling, ritual, evocation and thaumaturgy allow refinement, and even then, you need evocation for element expansion and you need thaumaturgy or evocation for specialization. Specifically:
Or, gain two additional specialization bonuses for Evocation and/or Thaumaturgy
Where each of the other casting powers explicitly permits Refinement, and is specific as to which options are permitted, Sponsored Magic does not, and in any case, the only refinement option that could be directly applicable to Sponsored Magic are the item slots (which I'd recommend allowing, on the basis of Sponsored Magic being 'Channeling + Rituals + flavor')