It is possible to parallel fuses and it is fundamentally safe (because a fault condition that exceeds the combined fuse rating will necessarily blow all fuses), but the carrying capacity of the fuses will not scale linearly. Meaning:
Let's say we're parallelling 4 fuses rated at 1A carrying, 5A guaranteed blowing capacity (both half-sine 10ms).
- These fuses will be guaranteed to blow at 5*4=20A
- These fuses will NOT be guaranteed to carry 4*1=4A. This will be somewhere between 1 and 4A (i.e. the carrying capacity of one fuse).
Statistically, you can take sqrt(n) as the guaranteed carrying capacity, i.e. about 2A. So all inrush and non-fault conditions should be guaranteed by design to be less than that, otherwise you will end up in a situation like you're in now, where possible one or two out of four fuses have blown.