  Using the recent results in the pure spinor formulation, we lay out a
ground-work towards the full momentum space amplitudes of open superstrings at
three-loop. After briefly reviewing the one-loop amplitude, we directly work
out the two-loop and reproduce the result that was obtained by a symmetry
argument. For the three-loop, first we use the two-loop regulator as a warm-up
exercise. The result vanishes. We then employ the regulator that has been
recently proposed by Aisaka and Berkovits (AB). It is noted that the terms in
higher power in $\frac{1}{\lambda\bar{\lambda}}$ that render the two-loop
regulator disqualified for the three-loop do not contribute. This with a few
other indications suggests a possibility that the AB regulator might also lead
to a vanishing result. Nevertheless, we argue that it is possible to acquire
the three-loop amplitude, and present a result that we anticipate to be the
three-loop amplitude.
