There are loads of possible ways to increase sensitivity, but none of them are easy or cheap given that the low hanging fruit was all picked off in previous generation detectors.
Increasing arm length is the "easiest" but definitely the most expensive option. Try finding a 40km L-shaped area that's seismically stable and free from significant anthropogenic activity. There may only be a handful of places in North America. However, 4km is already on the cusp of being long enough that gravity misaligns the two mirrors are each end of each arm due to the curvature of the Earth. Going to 40km would prompt the need for static corrections to mirror alignment, which will increase the amount of seismic noise that couples into the longitudinal direction in which gravitational waves are sensed. There are other problems such as the need to either refocus light at points along the arms (very susceptible to alignment and thermal noise) or use much, much bigger mirrors. The Advanced LIGO mirrors are already ~40kg, ~30 x 15cm cylinders of the purest fused silica known to man circa ~2012. There is talk of increasing the mirrors to 200kg and ~50 x 25 cm, and no facility is currently capable of producing pure enough fused silica at that size.
An "easier" option is to increase the laser power. This gives diminishing returns, and leads to an increase in high frequency sensitivity at the expense of low frequency sensitivity (due to photon pressure pushing the mirrors around noisily). However, the challenges are to make stable lasers that are also powerful - very tricky - and to mitigate the effect that laser absorption has on the mirrors within the interferometer - as you increase laser power, things heat up. Hot mirrors can lens the light, misaligning it and creating extra loss (i.e. reducing sensitivity). It's trickly to mitigate. Another effect of higher laser power is the introduction of parametric instabilities, where the mechanical body modes of the mirrors are amplified by the high laser power, leading to huge spikes of noise at narrow frequencies which are difficult to damp out.
Another is to use a different interferometer topology: instead of an L-shaped Michelson interferometer, suggestions have been made for Sagnac interferometers which possess an interesting property called quantum non-demolition, which can potentially reduce the limiting noise source in Advanced LIGO which directly increases sensitivity. Research into this is at a very early stage and will not be seen in detector facilities for decades, if ever.
So, the short answer is: there are lots of potential methods to increase sensitivity, but all of them are challenging and require significant R&D and money.
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.
"If we improve our detector sensitivity, by say a factor of two or three, the rates will go up from, you know, seeing one every month or every two months, to seeing one every day or every week."
- David Reitze, Executive director of LIGO
I don't know what their uptime is, but it sounds like they probably have a number of as-yet unreported observed events.
What is involved with increasing sensitivity I wonder? Is it purely lengthening the arms? or are there other advancements required?
Hopefully one day we can have these things in space, isolated from noise and curvature of the earth and no need for vacuum equipment.