Summary: An abelian 4D, \( \mathcal{N}=4\) vector supermultiplet allows for a duality transformation to be applied to one of its spin-0 states. The resulting theory can be described as an abelian 4D, \(\mathcal{N}=4\) vector-tensor supermultiplet. It is seen to decompose into a direct sum of an off-shell 4D, \( \mathcal{N}=2\) vector supermultiplet and an off-shell 4D, \( \mathcal{N}=2\) tensor supermultiplet. The commutator algebra of the other two supersymmetries are still found to be on-shell. However, the central charge structure in the resulting 4D, \( \mathcal{N}=4\) vector-tensor supermultiplet is considerably simpler that that of the parent abelian 4D, \( \mathcal{N}=4\) vector supermultiplet. This appears to be due to the replacement of the usual SO(4) symmetry associated with the abelian 4D, \(\mathcal{N}=4\) vector supermultiplet being replaced by a \(\mathrm{GL}(2 \mathbb{R}) \otimes \mathrm{GL}(2 \mathbb{R}) \) symmetry in the 4D, \( \mathcal{N} =4\) vector-tensor supermultiplet. The Mathematica code detailing the calculations is available open-source at the HEPTHoolsData Repository on GitHub.