<p>Unidirectional topological behavior, engendered by imposing topological operations winding around an exceptional point, is sensitive to dark modes, which allow deactivating topological operations, resulting in a complete blockade of both mode conversion and phonon transfer between dark and bright modes. Here we demonstrate how to beat this challenge and achieve a versatile yet unique nonreciprocal topological phonon transfer and blockade via dark-mode engineering. This happens by harnessing the power of synthetic magnetism, leading to an extraordinary transition between the dark-mode nonbreaking and breaking regimes, in a precise and controlled manner. Specifically, topological phonon blockade (transfer) happens in the dark-mode nonbreaking (breaking) regime, offering an exciting opportunity of switching between topological phonon blockade and its transfer on demand, which has no counterpart in previous studies. Remarkably, applying dark-mode engineering to quantum optomechanical networks can enable scalable network-based topological phonon transfer and quantum collective ground-state preparation. The proposed mechanism has general validity and can be generalized to the manipulation of various dark-state-related quantum effects, advancing the development of scalable quantum information processors. This study maps a general path towards generating a profoundly different topological quantum resource with immunity against both dark modes and dark states.</p>