  We study topological phase transitions in tetragonal NaZnSb$_{1-x}$Bi$_x$,
driven by the chemical composition $x$. Notably, we examine mirror Chern
numbers that change without symmetry indicators. First-principles calculations
are performed to show that NaZnSb$_{1-x}$Bi$_x$ experiences consecutive
topological phase transitions, diagnosed by the strong $\mathbb Z_{2}$
topological index $\nu_{0}$ and two mirror Chern numbers $\mu_{x}$ and
$\mu_{xy}$. As the chemical composition $x$ increases, the topological
invariants ($\mu_{x}\mu_{xy}\nu_{0}$) change from $(000)$, $(020)$, $(220)$, to
$(111)$ at $x$ = 0.15, 0.20, and 0.53, respectively. A simplified low-energy
effective model is developed to examine the mirror Chern number changes,
highlighting the central role of spectator Dirac fermions in avoiding symmetry
indicators. Our findings suggest that NaZnSb$_{1-x}$Bi$_{x}$ can be an exciting
testbed for the exploration of the interplay between the topology and symmetry.
