Not for every $\Delta$ there exists maximal dual $\Delta$-complex. E.g. a lattice simplex in $\mathbb{R}^{3}$, whose vertices are $(1,0,0)$, $(0,1,0)$, $(1,1,0)$ and $(0,0,n)$, cannot be further subdivided. On the other hand, a maximal dual $\Delta$-complex is, of course, not unique.