Using a Main Surge Protector for only branching out other surge protectors
I'll add to S. Binder's answer to just provide my experience with multiple surge protectors:

Observations:


A surge protector is also often viewed as an outlet strip or splitter &mdash; an easy way to get more outlets out of one.
Most modern protectors are reasonably good at doing what they're supposed to: protect. They include circuit breakers which are meant to limit how much power they supply.
With the plethora of small personal devices these days, in an office environment, I generally see surge protectors used to provide outlets for USB chargers, computers, monitors, network equipment, desk lamps, and so on. Most of these are low power devices, and even with every outlet on a surge protector occupied, the total power is well within safe limits.
All of that said, when someone plugs a 1500 watt space heater into the surge protector, it eventually (if not immediately) trips the breaker. Most basic surge protectors are only rated for 15A, which at 120V equates to 1800 watts. With other devices connected, a single heater will usually push things above the protector's limits.
In theory, a surge protector daisy-chained into one or more other surge protectors increases protection, because multiple circuit breakers are now involved. However...


Problems:


Casually, people don't think about total power on a given circuit. Multiple surge protectors offer "more outlets!" to the random passerby. This can result in people adding additional items to a circuit that may already be close to its limit. This can be dangerous if...
Surge protectors (or just "multiple outlet strips"), like anything else, can fail. If it has no circuit breaker, or is faulty, that can be the precursor to disaster ranging from a melted device to a burned-down building.
Because of the above two problems, most commercial or industrial areas will not allow them to be serially connected. (Inspectors will cite you.) It's not because of being intrinsically unsafe, it's that it invites improper loads to occur, which then tests the safety devices. The local fire marshal prefers situations where safety devices are not tested and not relied upon. Apply the same rules at home and don't "test" your homeowners or renters insurance.