Are you planning to use 2.4Ghz, 5Ghz or both? As you probably know already, 2.4Ghz (b/g/n) has 3 non-overlapping channels and 5Ghz (a/n) has more than 20 non-overlapping channels. There's no problem with one set of 5500's managing one set of LAPs and another set of 5500's managing another set of LAPs, the problem is radio interference. You could for example, run 2.4Ghz on one network and 5Ghz on another network, and then place two LAPs from two networks near each other, but in most cases, especially in hospital environments, you need 2.4Ghz support (802.11b, RFIDs). In your scenario if you are going to run 2.4Ghz on two separate WiFi networks, it will be pretty difficult to design it in such away that provides good coverage and little interference with 3 available channels.
Other folks here have plenty more experience with WLANs and could recommend some ideas.