If you just want to replicate the measurement folders within a new project from an existing project you can use the Based on feature when creating the new project.
If you don't want to create a new project, the only other way is to right-click on a measurement folder and select Copy Measurement.
You can then rename the folder. If all dimensions are the same as another folder, then that is all you'll need to do.
If the dimensions are different, you will need to clear out the copied dimensions and measure the new ones.
If it's the latter, it would be quicker to just create a new folder. This will only work one folder at a time. You can NOT copy multiple folders at once.