  We study symmetry-protected topological (SPT) phase transitions induced by
stacking two gapped one-dimensional subsystems in BDI symmetry class. The
topological invariant of the entire system is a sum of three topological
invariants: two from each subsystem and an emerging topological invariant from
the stacking. We find that any symmetry-preserving stacking of topologically
trivial subsystems can drive the entire system into a topologically nontrivial
phase. We explain this intriguing SPT phase transitions by conditions set by
orbital degrees of freedom and time-reversal symmetry. To exemplify the SPT
transition, we provide a concrete model which consists of an atomic chain and a
spinful nanowire with spin-orbit interaction and $s$-wave superconducting
order. The stacking-induced SPT transition drives this heterostructure into a
zero-field topological superconducting phase.

Mesoscale and Nanoscale Physics