Lately, on more than one blog (Grammarist as LoboSolo), I've stuck up for the word overexaggerate from those who believe that word either doesn't exist (it does) or that it is unneeded (maybe) or redundant (it's not). The word overexaggerate only highlights the befuddling that can come from brooking (using) long Latinates and why we should stick to brooking short Latinates or not brook them at all.
Let's start with why this word triggers the pendants to leap to the fight. In their eyes, exaggerate alreddy betokens, in their words, excessiveness. Therefore, since the excessiveness is built into the word, to add the forefast (prefix) over- is, well, excessive! And thus, redundant and therefore unneeded.
They're half-right. Let's take a look at the word exaggerate. In the 1530s the word first shows up in English. Exaggerate comes from Latin exaggeratus, the past participle of exaggerare meaning to heap up or pile on. Exaggerare itself comes from the forefast ex- + aggerare. Aggerare, in turn, comes from ad- (to, toward) + gerere (carry).
Is your head spinning yet? We're not thru with this wight yet!
So what does the forefast ex- do to it? In Latin, the forefast ex- onefoldly means 'out of' or 'from'. This is eathly seen in ex nihilo which means "out of nothing" and the legal term, ex parte which means from a side. Thus an ex parte hearing is where only one side is there to be heard. Later, ex- also began to be brooked as an intensifier ... one might say 'more' or 'thoroly'. For byspel, exacerbate means to make worse; exasperate is to "intensely infuriate".
In plain English, exaggerate means to truly pile on or heap up. Indeed, this is what it meant when it first came into English. It wasn't until the 1560s that it began to displaced overheap(en) as the verb for the sense of to overstate. Since both overheap and overstate alreddy have over- built into them, the pendants say putting over- onto exaggerate is like saying over-overheap. While it is true that we wouldn't say over-overstate, we wouldn't do so only because we don't like to say over-over... We can and do, however, say something like "greatly overstated".
Then can one overexaggerate? Without nay one can! What the pendants are overlooking is that we often blend and match forefasts. As we can see from above, the word exaggerate itself has two Latin forefasts onto the stem. So putting another forefast like over- onto a Latin root is ok. We do it often.
Next, does it make sense? Yes, it does. There are degrees of exaggeration. One can greatly exaggerate; one can excessively exaggerate; one can even overly exaggerate! If one can overly exaggerate then one can drop the overly and make it a forefast ... Thus one can overexaggerate.
It may be true that folks often say overexaggerate when exaggerate would do. But that is more a matter of style and the belief of the speaker.
My rede is to not brook either exaggerate or overexaggerate. There are many other ways to say it ... overheap, overplay, overstate, stretch, asf. where it is eath to see when and when not to brook over-.