Can injection moulding dies be changed?

Hello friends,
I would like to know if it is possible to modify an existing die from injection moulding. For example, if I find an obsolete plastic product and like the basic design but, so that it meets my needs, it would need some modifications (eg a couple of different holes or different-shaped holes), can this be done? If I were to approach the factory in China that has the mould, would they be able to modify it for me and produce my product? Or would it be necessary for me to start again from scratch. Obviously, I would save a lot of money if I were able to modify an existing product. Thanks in advance for your replies.

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