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From Home Guides:
Other friendly plants to place near asparagus include marigolds (Tagetes), comfrey, coriander and dill. These plants deter some insect pests, such as aphids, spider mites and other harmful species. Be careful when companion planting with these herbs and flowers, because while they are friendly for asparagus, they may not be friendly with other companion vegetables, such as tomatoes, planted with the asparagus. Make sure each plant is compatible with the others before placing them in the same areas.
Asparagus Antagonists
There are plants that you should not plant near asparagus because they offer no benefits and may hinder plant growth or attract harmful insects to the area. The plants to avoid placing near asparagus include garlic, onions and potatoes. Garlic and onions can inhibit the growth of asparagus and other plants, such as peas. You can still grow these plants in your garden, but plant antagonistic varieties away from the asparagus.