Consider the entire project for a moment. Understand that you will have a lot of things torn open, removing the flooring, the sink cabinet, etc. Wouldn't it be easier to do it all at once instead of possibly damaging your new floor or sink cabinet while trying to remove the old tub surround later? Also think about the mess, two messes instead of one. Not to mention your tools and all the materials, you will basically be doing things twice. If you are hiring someone, it could cost you a lot more to have them come back
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Tommy Bahama