  Various modified quantum teleportation schemes are proposed to overcome
experimental constraints or to meet specific application requirements for
quantum communication. Hence, most schemes are developed and studied with
unique methodologies, each with its inherent challenges. Our research focuses
on interconnecting these schemes appearing to be unrelated to each other, based
on the idea that the unique advantages of one scheme can compensate for the
limitations of another. In this paper, we introduce an asymptotic teleportation
scheme requiring the receiver to perform a classical selection task followed by
a quantum correction. This scheme bridges standard teleportation with
port-based teleportation through the transformation of joint measurements.
Specifically, we categorize and analytically investigate protocols within this
scheme for qubit systems. Given that linear optics teleportation protocol
without ancilla qubits is contained in the two non-trivial groups, we provide a
novel perspective on its expansion. Furthermore, we discuss the potential
application of a protocol from one of these groups as a universal programmable
processor and extend these protocols to higher-dimensional systems while
maintaining the same properties and potential, providing the analytic form of
the joint measurement and its performance. These results thereby propose new
avenues for developing a quantum network in higher-dimensional systems.
