Many companies offer private label services, but the quantities can be pretty steep. You can choose to relabel your garments personally or find a sewing service to do the job.
If you choose to relabel, keep in mind, that there are different methods. In one case, depending on the construction of the garment, it may mean sewing your label ABOVE the seam and cutting away the original label. The preferred method in my opinion and if the garment will allow, entails opening the neck seam, removing the original label, inserting the private label and sewing the seam closed.
Article 1 sells shirts with a tear out label. You can then hire a sewing service to sew in your private labels or have your screen printer print a label on the inside neck.
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