Answer: You can grow everything under row covers or screens, providing you're willing to take on the job of hand pollinating each flower your plants produce. Green leafy vegetables and most root crops do not insect activity, and therefore can remain under row covers all season long. Green beans are self-fertile, so no special treatment is needed, other than shaking the plants periodically to help the pollen connect to the proper parts of the flowers. All other flowering plants should be hand pollinated to assure they'll set fruit. You can take a soft artist's brush and 'visit' each open blossom to transfer pollen.
Good luck with your gardening venture!
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