Construction systems for constructing a structure on a foundation and methods relating thereto are disclosed. In an embodiment, the construction system includes a rail assembly configured to be mounted to the foundation. In addition, the construction system includes a gantry movably disposed on the rail assembly configured to translate along a first axis relative to the rail assembly. Further, the construction system includes a printing assembly movably disposed on the gantry and configured to translate along a second axis relative to the gantry. The second axis is orthogonal to the first axis. The printing assembly is configured to deposit vertically stacked layers of an extrudable building material on the foundation to construct the structure. The gantry has a width along the second axis that is configured to be adjusted relative to the foundation.