Why can't Fourier Transforms be used to extend data sets?

Question

I have been trying to have some python code take some wave created by adding sine waves together, which has some number of samples and computing a discrete Fourier transform to get the frequencies of these sine waves. I then want to use these frequencies to make a wave that consists of the same frequencies of the original wave but extended by some amount. I can't seem to find a way to do this, so is it a limitation of the library I'm using or is there some mathematical reason I can't do this? My primary knowledge with regard to Fourier transforms is to do with continuous Fourier transforms and I can't see any reason why you couldn't do what I am trying to do with these.