Wiki 2 Admits same day

If it's for the same problem, no you can't.

We combine the previous discharge and subsequent admission into a subsequent inpatient visit, based on documentation. Then bill out the discharge when they later leave. They lose out on the re-admission charge if it's for the same problem.

If it's for an entirely different problem (like the discharge was for an MI, and the admission was for a hip fracture), then you can bill both, but you'll have to fight for your money by providing clear documentation of the different diags.
For the discharge/admit same day, bill a round, then when the patient goes home after that, bill the discharge.