After being presented by Molodtsov [1], soft set theory became well-known as a cutting-edge method for addressing uncertainty-related issues and modeling uncertainty. It may be used in a range of theoretical and practical applications. The soft binary piecewise plus operation is a novel soft set operation presented in this work. Its fundamental algebraic properties are investigated in detail. Additionally, the distributions of this operation over several soft-set operations are examined. We establish that the soft binary piecewise plus operation is a right-left system and, under some assumptions, a commutative semigroup. Furthermore, by taking into account the algebraic properties of the operation and its distribution rules together, we demonstrate that the collection of soft sets over the universe, together with the soft binary piecewise plus operation and some other types of soft sets, form many important algebraic structures, like semirings and near semirings.