You should not daisy chain protective devices (fuses, MOVs, breakers, etc.) without first doing the appropriate research because generally speaking, they are rated to interrupt in x seconds given a particular fault current. When you have two protection devices with similar ratings in the circuit, they end up both trying to interrupt and may very well end up interfering with each other's interruption capability, possibly to the point where neither will properly clamp or interrupt the fault, causing excessive current flow and possibly fires.
e.g. A fuse chosen more or less at random will clear in 1s with a ~20A fault current. If you have a second fuse with similar ratings in series, they will actually start limiting the fault current as they open up, and the fault current is no longer 20A, it may be 15A, or 10A, or ... you get the idea. That same fuse will clear a 10A fault in ~10s, which could be enough time to heat up wire or traces or cause a semiconductor to fail because it wasn't designed to handle that kind of current for that kind of time.
e.g. A MOV series chosen more or less at random will clamp a surge at 130V. Two in parallel will have (slightly or significantly) different clamping voltages, usually with the lower one "winning". The breaker/fuse and MOV are usually selected so that the MOV will clamp and the breaker will open with the surge current, but when you mix and match you end up with a MOV clamping earlier, which the fuse/breaker wasn't designed to trip at, which now alters its fault ratings, leading to unpredictable protection.
In the industrial power world this kind of interaction is actually a significant part of the overall electrical design, since you have substation transformers protected with fuses, and the downstream equipment protected with their own fuses or breakers, and then the load controllers protecting their semiconductors or motors again with their own protective devices, usually a combination of MOVs or fused MOVs and either breakers or fusing. There's a lot to look at, including the I2T ratings of the protective devices, interrupting capabilities, pulse withstand capabilities, temperature derating, clearing times, current limiting effects as the devices become active, Joule ratings and so on. Here are a few good references if you wish to look into it further. The term "fuseology" has come about to describe this particular aspect of electronics design.
... and I bet you thought fuses, breakers and TVS type devices were pretty simple, didn't you. :-)