I currently have one WS-C3560G-48TS that is the single connection point between three floors. I do indeed have 4hour support on the equipment however I am interested in gaining knowledge on the possibility of a switch failover scenarios; so if one 3560 fails the entire building will not suffer.
The model you have is a pretty reliable workhorse although it's most commonly seen as an access switch and not a core or distribution switch.
In a core where high availability is a concern we would normally use at least a dual power supply unit and most often more than one switch with dual uplinks from the core to each access layer switch. The most common cause of failure (after human errors) is loss of power. If you have a dual power supply or two core switches, make sure they are plugged into outlets fed from separate breakers at a minimum.
More modern switches can be combined using various methodologies such as stacking (newer Catalyst 2k and 3k series), virtual switching system or VSS (Catalyst 4k or 6k series), and VPC (Nexus 5k and 7k). The first two give you a single control plane - managing multiple units as one.