Center to Advance Palliative Care

I am a new hospice medical director and the question I have is how to receive reimbursement for patients who are under 65 (no medicare or medicaid), on hospice and have private insurance (Bluecross, Aetna etc.). My hospice does my billing and pays 100% of the invoice to me (for Medicare and Medicaid patients) but does not process physician invoices for the private insurance patients. Do I need to contract separately with the insurance companies or are there other options? This will continue to be a problem as our field grows and more patients are referred to both hospice and palliative care at a younger age.