> It probably is; it's quite common for fair numbers of hospital staff

Sort of, yes - in NYC, nurses are almost all members of 1199SEIU, for example, and the shift-work nature of nursing makes it easy for them to be employed simultaneously by multiple hospitals. Though my point is that this is usually handled on an individual level (by the nurses who choose where to work), rather than the hospitals themselves directly coordinating staff schedules in tandem.