The Collatz map T(n)=n/2 for even n and T(n)=3n+1 for odd n admits classical affine descriptions via parity vectors, but these typically compress each odd event into the macro-step (3n+1)/2, obscuring intermediate algebraic states. We introduce a two-stage expansion that separates an odd event into a rewrite step R (expressing n=2x+1) followed by a forced follow-up C (sending x↦3x+2), alongside the even halving step E. This yields a word system over {E,R,C} and a uniform normal formX_N (w)=(3^k(w) X_0+2^D(w) -3^k(w) +σ_N (w))/2^D(w) ,where σ_N (w) admits an explicit signed monomial expansion in powers of 3 and 2. We prove that complete two-stage words (those with every R immediately followed by C) compress under RC↦O to the standard parity-vector affine form, giving a precise equivalence criterion and a canonical matching rule (k,D,Σ). Consequently, removing the standard-image equations from the two-stage enumeration leaves exactly the truncated (dangling-R) equations corresponding to intermediate states not representable in the standard form. Finally, we derive residue-class "locking" conditions modulo 2^D(w) , clarifying integrality constraints and connecting the framework naturally to 2-adic formulations.