You certainly may have multiple subnets on a single router. You may have multiple subnets on a single interface. If your router interface is connected to a trunk port on a switch (you would be doing intervlan routing on the router for the switch) you would configure multiple subinterfaces on the interface, each subinterface would be for one of the VLANs on the switch and each subinterface would be a separate subnet. Or if the router was not connected to a switch trunk then you could configure 1 primary subnet and could configure multiple secondary subnets using the secondary address feature.
