In this paper, we introduce the construction of extending a soft topological space with respect to a family of soft subsets from a given soft topological space. We focus on studying this extension when the family consists of a single soft set. We show that the extended soft topological space is not uniquely determined. We further study the conditions under which certain soft topological properties are shared between the extended soft topology and the original one. Lastly, applying a soft point theory, we see that the obtained results are parallel to those results that exist in classical topology, and by Terepeta's Theorem, our results are natural generalizations.