Since stock is in the cabbage family, all the same pests that apply to cabbages and broccoli are your problem insects. That includes aphids, cabbage looper/moth, cabbage webworm, cross-striped cabbage worm, diamondback moth, imported cabbageworm, harlequin bug, among others.
This year I am going to try systemic Neem Oil treatment to some of my outdoor plants to hopefully kill all the destructive pests but leave my predators alone. My backyard has a healthy population of Preying Mantis and I’m working on increasing the Lady Bug population.
Side note – remember to not use Neem Oil anywhere around your butterfly garden since the wonderful Monarch Butterfly Caterpillars do eat the Milkweed plants. These plants are being sacrificed to the hungry “cats” as they were grown to do!