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Raised beds, collecting rainwater as well. - perhaps tiered beds can have a French drain at the end that catches excess water run off from the rain. It would be a larger area to collect rain water and would only be extra If the other plants were all watered.
If downspouts and regrading don't cure your damp basement, the most effective solution may be a drainage system and sump pump, which will collect and pump the water away from the house.