Sensitivity is about picking out a signal from the noise. The way you increase sensitivity is to decrease the noise. Effectively this means isolating the environment of the LIGO experiment and a great deal has been done on this. If you search arXiv for LIGO over the past two decades, you'll find plenty of articles on this, but I warn you, you may be reading about injecting null energy modes into the system in one paper while reading about mirror design and reflection results in the next paper.