Midi-chlorian counts did not indicate an upper limit to Force ability; the possibility existed for a Jedi to achieve a connection to the Force on an equivalent level to a Jedi with a higher count.1
It was attempted however, in the final novel of the Clone Wars story arc, "Yoda: Dark Rendezvous," we learn that there was forbidden experimentation on midi-clorians conducted by the Nobles on the Sith refuge of Vjun in an attempt to increase force sensitivity. Their experiments were unsuccessful, and drove the entire population of Vjun mad.
There were Sith who were successful with Midi-chlorian manipulation. Emperor Palpatine's Sith Master, Darth Plagueis, was a master of midi-chlorian manipulation to the degree that he could heal himself when wounded, prevent himself from aging, restore life to the dead, and even cause animals to give birth without a partner. It was Plagueis experiments with the midi-chlorians that caused the immaculate conception of Anakin Skywalker. Plagueis tried to create a being out of the midi-chlorians, but assumed he had failed, but what had actually happened was the Force itself responded to the attempt by creating the one who would destroy the Sith.
It is possible that the Sith could have eventually found a successful method of harvesting midi-chlorians to inrease their force sensitivity–the immortal Plagueis would probably have eventually figured it out if Palpatine hadn't killed him–but after the creation of the Empire, all research on midi-chlorians was made illegal.
1. wookieepedia: Midi-chlorian Biology.
Random fact: midi-chlorians are real! (see Midichloria on Wikipedia). It's a recently discovered organism that was found inside the mitochondria of cells. The scientist that discovered it asked George Lucas for permission to name it midi-chlorian and Lucas consented.