Depending on what you are growing, you could probably leave the white plastic on and put shade over the top. I'm with Ray on the shade, it always goes on top, you can take it off in the winter if you need to. I'm about 5 USDA zones north of you, not going to guess on the percentage. I'd start with 40% and add another layer if it was still too bright.
White plastic is an acceptable option for greenhouse covering in some climates. Probably not for me, but I've thought about it a few times for the foliage house... not that I have a foliage house yet, but maybe soon.
4mil plastic is almost certainly too thin. It won't last very long. If you don't mind putting new plastic on every year it might be ok, but even so, you don't want your plastic ripping in January when the winds blow from the north. Get a good plastic, UV treated. It isn't that expensive from a greenhouse supply company. Some of the slightly more expensive plastic will last 5+ years.
Rob
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