Quasitoric manifolds (QTMs) are smooth compact manifolds admitting a well-behaved action of the compact torus so that the quotient of this action is diffeomorphic (as a manifold with corners) to a combinatorially simple polytope.  We'll develop a procedure to attempt to view any QTM as a codimension 2 subquasitoric manifold of an "ambient" wedge QTM.  We formulate these wedge QTMs on the level of polytopes from the wedge polytopal construction.  The existence of such wedge QTMs in the general case is still unknown but we'll demonstrate a proof for the existence of such constructions for any Bott tower and discuss a similar conjecture concerning Bott manifolds and connected sums of the aforementioned.  We will focus on small dimensional examples to view these constructions.