I recently heard one of my relatives is applying to two similar positions at the same institution, both administrative I believe. I'd always heard you shouldn't do this since it could come off as desperate or overconfident and decrease your likelihood of working for that institution, but maybe I'm missing a valuable job search strategy. Is it ever okay to apply to two similar jobs at the same place?
I think it depends on the institution itself and how the institution treats the recruitment process.
If it is a small firm, the Human Resources department will be very small or inexistent, probably only one person will read your relative's applications and they will receive only a few CVs; therefore, the strategy will not be the best one. However, in a large firm, the two applications may probably be read by different people, or the same person may have to read hundreds of CVs and will have forgotten the first one by the time he/she reads the second one, so in those cases, your relative may be lucky.
This may work for administrative or clerical positions. On the other hand, I wouldn't recommend it for technical jobs, where it will seem really strange to apply both for, let's say, a mechanical and an electrical engineer position at the same time. This conveys the feeling that you are really desperate and/or you don't know what you are good at.