Radish
Radishes size up in about a month and are pulled long before endive rosettes close over the bed, so the two rarely compete; the radish taproot also works a deeper slice of soil than endive's shallow feeding roots.
Carrot
Carrots send a single deep taproot well below endive's shallow mat of feeder roots, so the two can share a row without fighting over water. Keep carrots on the sunny side, since endive leaves spread wide.
Strawberry
A low mat of strawberry leaves shades the soil surface and slows drying, which suits endive's need for steady moisture. Leave 12 inches of clear ground around each head so air still moves through the crown.
Garlic
Garlic's strong smell can help hide endive from aphids that locate host plants by scent, and under low pest pressure a garlic edging often reduces early colonies. Do not expect it to stop a heavy infestation.
Chervil
Let a few chervil plants flower and their small flat flower clusters feed hoverflies and tiny parasitic wasps, whose larvae hunt aphids on nearby endive. Chervil also stays low and shade-tolerant, so it does not crowd the heads.