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Ok today I tried the system to see how much sound would come out of her. When the volume was up around 47 the passenger's side speakers front and rear stopped altogether until I turned the h'unit off and on again. Oh yeah I checked and I have 60 watt three ways in the front and 30 watt cheap pioneer subs in the parcel shelf. It's always the left hand side that cuts out and/or stops.In short theres no "limit" on wattage speakers that you can run off the head-unit.
If you were to go out and buy 100wrms (something like 300w max i suppose) speakers and mounted them properly, when they start to distort its more than likely not the speakers distorting, its the head-unit thats sending the speaker a distorted signal. So basically what im saying is you wont get the maximum volume out of those speakers when running them off the head-unit.
Probably this is whats happening at the moment with your speakers, but "cut in and out slightly" dosent sound like distortion, it sounds more like theres a speaker wire touching metal or each other a tiny bit, and only becomes a problem when theres a more current passing through. Its hard to diagnose though over the net.
I'd be checking the wiring at the speakers first.
How did you connect the wiring to the speaker?