  We compute the superconformal partial waves of the four-point correlator
$\langle JJJJ\rangle$, in which the external operator $J$ is the superconformal
primary of the $4D$ $\mathcal{N}=2$ stress-tensor multiplet $\mathcal{J}$. We
develop the superembedding formalism for the superconformal field theories
(SCFTs) with extended supersymmetry. In $\mathcal{N}=2$ SCFTs, the three-point
functions $\langle \mathcal{J}\mathcal{J}\mathcal{O}\rangle$ with general
multiplet $\mathcal{O}$ contain two independent nilpotent superconformal
invariants and new superconformal tensor structures, which can be nicely
constructed from variables in superembedding space, and the three-point
functions can be solved in compact forms. We compute the superconformal partial
waves corresponding to the exchange of long multiplets using supershadow
approach. The results are consistent with the non-trivial constraints by
decomposing the $\mathcal{N}=2$ superconformal blocks into $\mathcal{N}=1$
superconformal blocks. Our results provide the necessary ingredient to study
the fascinating $4D$ $\mathcal{N}=2$ SCFTs using conformal bootstrap.
