"Plethora" is something of an "educated" word, and so not something you should use lightly, without considering whether your audience will understand what it means, or whether it sounds pretentious rather than erudite.
That being said, you can have a "plethora" of anything that makes sense. Because "plethora" is synonymous with "overabundance", it would normally be of something positive -- but the excess amount makes it an annoyance, hassle, or obstruction. A "plethora" of shoes, or coins, or texts is fine if you would normally consider these to be good things in moderation, but a problem if you have too many.
In other words, "plethora" doesn't just mean "a lot". It means "more than you can handle". For example, I might say I have a "plethora" of job offers -- something that's usually good to have, but when I have too many it's hard for me to find the best one.
For this reason, something like a "plethora of complaints" is unusual. In the right context the contrast can be humorous or satirical, but you have to explain it properly. For example, I found this headline:
Congress approaches EC with plethora of complaints.
My personal opinion is that this is awkward, as there seems to be no ironic context. Here "plethora" simply implies "more complaints than the EC can handle". I would prefer another word more often associated with a negative excess, such as slew:
slew (n): 3. A large number or quantity of something. Congress approaches EC with a slew of complaints