We consider the stability of the drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape. Flows of this type are fundamental in the fabrication of micro-structured optical fibers that have the revolutionized the transmission of data and are extremely important in modern sensing. The thread evolves due to a complicated interaction between axial drawing, inertia, surface tension, thermal and pressurization effects. Despite the complicated geometry of the boundaries, we use asymptotic techniques to determine a particularly convenient formulation of the equations of motion that is well-suited to stability calculations. We use this formulation to show how the presence of internal holes affects the stability of the drawing process and address a longstanding question from the literature. We also consider the interactions between external cooling, surface tension and inner hole pressurization and show that these effects combine in a complicated way to produce counterintuitive behaviour. We carefully explore these effects and explain the underlying mechanisms.