Abstract This paper studies several aspects of symbolic (i.e. subshift) factors $\mathcal {S}$ -adic subshifts finite alphabet rank. First, we address a problem raised by Donoso et al [Interplay between topological rank minimal Cantor systems, S-adic and their complexity. Trans. Amer. Math. Soc. 374 (5) (2021), 3453–3489] about the prove that this is at most one extension system, improving on p...