split-shared visits as a consultation

We are trying to find information to present for a provider about billing split-shared visits. We know Medicare does not accept consult codes so it is billed under the inpatient codes 99221-99223 for initial visit and 99231-99233 for subsequent. But if the intent is for a consult can you bill the inpatient initial visit using a split-share note? Meaning the Mid-Level does the Review of Systems and History with the physician on the same day doing the HPI, exam and assessment.

If it is not Medicare can it be billed as a split share consult using the CPT® consult codes?

Thank you in advance for any information.
Debbie