Usage of 'plethorically'

Solution 1:

Yes, it can.

First, "plethorically" absolutely is a word (Click the link and scroll down to "Related Forms").

Second, in my estimation, you've used it correctly.

To be fair, I did question whether it could be used with a noncount noun, but I see in the example given at the above link that "plethoric" is used to describe the noncount noun "speech," so it could likewise properly be used to describe the noncount noun "obnoxiousness." Ergo, as an adverb (i.e., "plethorically"), it follows that it could properly modify the adverbial form "obnoxious."

There is no restriction on the use of that word from terms that modify "biotic entities," human or otherwise.

ALL OF THAT SAID, I would steer clear of saying the following:

My fellow classmates are plethorically obnoxious, as they loquaciously spew ludicrously nonsensical drivel.

Why? Because it is plethorically loquacious and ludicrously obnoxious, never mind drivelingly redundant.

Setting aside the whole trying-way-too-hard aspect of it that makes it seem as though you drafted this by using a thesaurus to change every word you could to make yourself seem smarter than you are, what you're saying is tantamount to this:

My fellow classmates are overflowingly offensive, as they with overflowing chatter overflowingly spit crazily meaningless chatter that's meaningless spit.

Granted, if those who hear or read this are stupid, they may not catch it, but if anyone who isn't stupid hears or reads this, you may abruptly find yourself on the receiving end of a comeback that will make you look stupider than everybody for hypocritically and ignorantly—and so ironically—doing EXACTLY what you're accusing your fellow classmates of doing while you in saying so quite laughably operate under a pretense that you are somehow better, which you're not, of course, as evidenced by what you just said that does everything you accuse your fellow classmates of doing and worse, just with $5 words instead of 50¢ ones.

To be clear, I'm not saying this to ridicule you but am saying this to try and save you from ridicule.

Solution 2:

First off, Plethorically isn't even a standard word.

See this ngram. It's not even listed as a word derivative in Oxford

So no, I wouldn't use it if I were you.

Now for using it with obnoxious:

"plethorically means an excessive or overabundant amount of something": No it doesn't. You're thinking of plethora. And maybe it's just me, but "a plethora of obnoxiousness" just sounds weird.

Word of advice: don't use too many big words. It's off-putting. Write to express, not to impress.