  A growing body of observational evidence suggests that the luminosity,
photometric shape and amount of rotational or anisotropical support in
elliptical galaxies may provide vital clues to how they formed. Elliptical
galaxies appear to fall into two distinct categories based on these parameters:
bright, boxy shaped, with little or no rotation, and less luminous, disky
shaped with significant rotation. One viable formation scenario is the ``Merger
hypothesis,'' in which two disk galaxies merge to form a new elliptical galaxy.
A comparison of the luminosity, photometric shape, and amount of rotation in
advanced merger remnants may shed more light on the possible formation
scenarios of elliptical galaxies. Yet, little observational data exists for
such merger remnants. This paper is the third in a series investigating the
photometric and kinematic properties of a sample of 51 optically selected
advanced merger remnants. Presented here are K-band isophotal shapes and
spatially resolved kinematics for a sub-sample of 37 merger remnants. The
results show that ~ 11% of the sample are boxy, and anisotropically supported
while ~ 47% are disky, and rotationally supported. The remainder of the sample
show variations among expected correlations between shape and rotation. This
may suggest that the isophotal shapes are still ``in flux.'' There does appear
to be a lower limit to the amount of anisotropy observed in the merger
remnants. This may provide an observational diagnostic for discriminating among
formation scenarios in elliptical galaxies.
