  We provide extended evidence that mode-coupling theory (MCT) of supercooled
liquids for the ${\mathsf F}_{12}$ schematic model admits a microscopic
realization based on facilitated spin models with tunable facilitation.
Depending on the facilitation strength, one observes two distinct dynamic glass
transition lines--continuous and discontinuous--merging at a dynamical
tricritical-like point with critical decay exponents consistently related by
MCT predictions. The mechanisms of dynamical arrest can be naturally
interpreted in geometrical terms: the discontinuous and continuous transitions
correspond to bootstrap and standard percolation processes, in which the
incipient spanning cluster of frozen spins forms either a compact or a fractal
structure, respectively. Our cooperative dynamic facilitation picture of glassy
behavior is complementary to the one based on disordered systems and can
account for higher-order singularity scenarios in the absence of a finite
temperature thermodynamic glass transition. We briefly comment on the relevance
of our results to finite spatial dimensions and to the ${\mathsf F}_{13}$
schematic model.
