  We consider a hitherto unexplored setting of stacked multilayer
($\mathcal{N}$) Lieb lattice which undergoes an unusual topological transition
in the presence of intra-layer spin-orbit coupling (SOC). The specific stacking
configuration induces an effective non-symmorphic 2D lattice structure, even
though the constituent monolayer Lieb lattice is characterized by a symmorphic
space group. This emergent non-symmorphicity leads to multiple
doubly-degenerate bands extending over the edge of the Brillouin zone (i.e.
Quadratic Band Crossing Lines). In the presence of intra-layer SOC, these
doubly-degenerate bands typically form three $\mathcal{N}$-band subspaces,
mutually separated by two band gaps. We analyze the topological properties of
these multi-band subspaces, using specially devised Wilson loop operators to
compute non-abelian Berry phases, in order to show that they carry a higher
Chern number $\mathcal{N}$.
