Dy2Ti2O7 is a pyrochlore antiferromagnet that has a partial magnetization plateau between 0.1 and 0.9T for magnetic fields applied along the [111] direction. This represents a dimensional reduction from the well known three-dimensional spin ice state to the less commonly studied kagome ice state. The magnetic field - temperature phase diagram shows several crossover lines and a clear first order phase transition in field around 0.9T. This terminates in what appears to be analogous to a liquid-gas critical endpoint at 0.35K. Studies of kagome ice systems and the dynamics of partial magnetization plateaux are very rare. We propose to investigate both phenomena by carrying out longitudinal field muSR measurements on Dy2Ti2O7 with the field applied along the [111] axis.