We present a weak-lensing analysis of the merging Frontier Fields (FF) cluster Abell 2744 using new Subaru/Suprime-Cam imaging. The wide-field lensing mass distribution reveals this cluster is comprised of four distinct substructures. Simultaneously modeling the two-dimensional reduced shear field using a combination of a Navarro-Frenk-White (NFW) model for the main core and truncated NFW models for the subhalos, we determine their masses and locations. The total mass of the system is constrained as M sub(200c) = (2.06 + or - 0.42) x 10 super(15)M sub(middot in circle). The most massive clump is the southern component with M sub(200c) = (7.7 + or - 3.4) x 10 super(14)M sub(middot in circle) followed by the western substructure M sub(200c) = (4.5 + or - 2.0) x 10 super(14)M sub(middot in circle) and two smaller substructures to the northeast M sub(200c) = (2.8 + or - 1.6) x 10 super(14)M sub(middot in circle) and northwest M sub(200c) = (1.9 + or - 1.2) x 10 super(14)M sub(middot in circle). The presence of the four substructures supports the picture of multiple mergers. Using a composite of hydrodynamical binary simulations we explain this complicated system without the need for a "slingshot" effect to produce the northwest X-ray interloper, as previously proposed. The locations of the substructures appear to be offset from both the gas ((ProQuest: Formulae and/or non-USASCII text omitted) arcsec, 90% CL) and the galaxies ((ProQuest: Formulae and/or non-USASCII text omitted) arcsec, 90% CL) in the case of the northwestern and western subhalos. To confirm or refute these findings, high resolution space-based observations extending beyond the current FF limited coverage to the west and northwestern area are essential.