  The basic \emph{entanglement swapping protocol} allows to project two qubits,
which have never interacted, onto a maximally entangled state. For
deterministic swapping, the key ingredient is the maximal entanglement that was
initially contained in two pairs of qubits and the capacity of projecting onto
a Bell basis. Thus the basic and deterministic entanglement swapping scheme
involves three maximal level of entanglement. In this work we propose
probabilistic entanglement swapping processes performed with different amounts
of initial entanglement. Besides that we suggest a non Bell measuring-basis, to
introduce a third entanglement level in the process. Additionally, we propose
the \emph{unambiguous state extraction scheme} as the local mechanism for
probabilistically achieving the EPR projection. The combination of these three
elements allows us to design four strategies for performing probabilistic
entanglement swapping. Surprisingly, we find a twofold entanglement threshold
effect related to the concurrence of the measuring-basis. Specifically, the
maximal probability of accomplishing a EPR projection becomes a constant for
concurrences higher than or equal to threshold entanglement value. Thus, we
show that maximal entanglement in the measuring-basis is not required for
attaining the EPR projection.
