This depends on the carrier, the packaging, the value of the shipment and your appetite for risk. Certainly, many shippers do not hesitate to place two or three fragile labels on an especially important box. Often, these will be of different types – to gain more attention. A label might be placed on the top of the box with others on the sides.
We are a label vendor, so it may seem hard for us to understand our biases regarding the number of labels used. Certainly, you do not want your shipments to arrive looking like the old 60’s van after a cross-country trip. Yet, labels are inexpensive. There is little downside to adding a few more fragile label warnings – just to make sure that your important message is not lost.