"Over-damped" implies there is an optimal amount of damping. At one time, the Linn Sondek and Oracle Delphi were considered the two best tables available. Their designs could not have been more different; the Oracle employed damping (particularly of the LP by it's mat), the Linn not. They sounded very different, people preferring one to the other. Was the Oracle over-damped, or the Linn under-damped?
A table's design is a combination of many different elements, offered as a complete package by it's designer. Perhaps it's better to leave a given design as is, and if one wants a more or less damped table, get one designed as such.
But as a mechanical transducer, why would one want the table itself to add vibrations or resonances of it's own to the tiny vibrations contained in the LP groove? There was a table designed from the ground up, done as a research project at an engineering college in England. A fundamental element of it's design is a trough of damping fluid, in which a little hollow tube attached to the tonearm's headshell is immersed. This damping system greatly reduces the resonant frequency inherent in all tonearm/cartridge pairings, as well as absorbing and dissipating any stray vibrations and resonances in the cartridge body and tonearm. It also, very importantly, "locks" the front end of the arm to the table, just as the bearings do at the rear of the arm. Robert Greene called the original Townshend Rock Turntable a legend in TAS, and the latest version of the table (Mk.7) just went out of production, a new version promised soon. One of the best kept secrets in Hi-Fi! Is it over-damped? Or are all other tables under-damped?