Possibly. But you would probably have to change some of the fundamental characteristics of the breed to do it.

Thoroughbreds today have lost the ability to carry weight over distance. That is because they have been bred for longer, finer legs, which increase stride and reduce weight. But along with that comes leg weaknesses due to decreased bone and longer cannons.

Thoroughbreds are also sprinters. Flat races rarely extend beyond 2-3 miles. The musculature required for such activates is actually different. Muscles designed to contract quickly and powerfully are fast twitch fibers. They produce quick bursts of speed and strength, but tire quickly. Slow twitch fibers contract more slowly, but will continue working over long periods. In order to breed a faster animal over the same distance, you will actually have to breed for different musculature, and you will lose either one or the other in proportion.

Thoroughbred racers also tend to have some physiological differences that help a dead run, but are not so helpful at other gaits.