Only five binary systems have been found to emit at TeV energies. Each of these systems is
composed of a massive O or B type star and a compact object (black hole or a pulsar). The
type of compact object and the origin of the gamma-ray emission is unknown for most of these
systems. Extending spectral observations to higher energies can help disentangle the nature of
the compact object as well as the particle acceleration mechanisms present. Interestingly, the TeV emission from these systems does not always coincide with their emission in GeV or X-ray, which is how many such systems have been originally discovered. Increased coverage of these systems may allow HAWC to see precisely when in the orbit the TeV emission begins and ends. The HAWC Observatory detects TeV gamma-rays with high sensitivity, covering over two-thirds of the overhead sky every day. Applying a stacking method to known TeV binary systems can help HAWC enhance the signal from TeV binaries above the steady background from other sources in the galaxy. We will present results from this stacking analysis using 760 days of HAWC data.