If you really wanted to, you could. Ideally if you wish to keep a barrel cactus to a single barrel with no off-shoots, the earlier you can remove the shoots, the better. On this cactus, due to the size of the off-shoots, removing them will leave an obvious scar, turning a nice cactus into an eye sore. If that doesn’t concern you, then gently remove the shoots and keep an eye on the scare to ensure no signs of diseases develop.
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