  We study the nature of quantum phase transitions out of $\mathbb{Z}_4$
ordered phases in quantum loop models on a zig-zag ladder. We report very rich
critical behaviour that includes a pair of Ising transitions, a multi-critical
Ashkin-Teller point and a remarkably extended interval of a chiral transition.
Although plaquette states turn out to be essential to realize chiral
transitions, we demonstrate that critical regimes can be manipulated by
deforming the model as to increase the presence of leg-dimerized states. This
can be done to the point where the chiral transition turns into first order, we
argue that this is associated with the emergence of a critical end point.
