To exaggerate, overemphasize, overstate. An idiom. The 'over' is added unnecessarily and its usage is virtually always synonymous with a mere 'exaggerate', rather than a different word, as 'exaggerate' is not a neutral usage verb like the word 'do'. There is no threshold for the word 'exaggerate', so it is not possible to overdo. To 'overexaggerate' is to 'overoverstate'.
Only idiots say overexaggerate.
To go beyond anticipated exaggeration.
Loren overexaggerated when she claimed she exaggerates a million times a second, when previously she stated, "I exaggerate 100 times a day."