  Within the framework of mode-coupling theory, the glass-transition scenario
is investigated for a system of particles interacting with a hard-core
repulsion and an additional square-shoulder soft core at larger distances. The
static structure is calculated from the potential in Percus-Yevick
approximation. For certain widths of the shoulder, the exponent parameter
lambda along the glass-transition line shows a double peak. At both peaks,
lambda can reach unity indicating the existence of higher-order
glass-transition singularities. It is shown that these higher-order
singularities originate from a line of avoided glass-glass transitions.
