Vivi Tsalmantza and I have found many double redshift in the SDSS spectroscopy (a few examples are published here but we have many others) by modeling quasars and galaxies with a data-driven model and then fitting new data with a mixture of two things at different redshifts. We have found that finding such things is straightforward. We have also found that among all galaxies, luminous red galaxies are the easiest to model (that's no breakthrough; it has been known for a long time).
Put these two ideas together and what have you got? An incredibly simple way to find double-redshifts of massive galaxies in spectroscopy. And the objects you find would be interesting: Rarely have double redshifts been found without emission lines (LRG spectra are almost purely stellar with no nebular lines), and because the LRGs sometimes host radio sources you might even get a Hubble-constant-measuring
golden lens. For someone who knows what a spectrum is, this project is one week of coding and three weeks of CPU crushing. For someone who doesn't, it is a great learning project. If you get started, email me, because I would love to facilitate this one! I will happily provide consultation and CPU time.