  Let $F$ be a $p$-adic field of characteristic 0, and let $M$ be an $F$-Levi
subgroup of a connected reductive $F$-split group such that $\Pi_{i=1}^{r}
SL_{n_i} \subseteq M \subseteq \Pi_{i=1}^{r} GL_{n_i}$ for positive integers
$r$ and $n_i$. We prove that the Plancherel measure for any unitary
supercuspidal representation of $M(F)$ is identically transferred under
\textit{the local Jacquet-Langlands type correspondence} between $M$ and its
$F$-inner forms, assuming a working hypothesis that Plancherel measures are
invariant on a certain set. This work extends the result of Mui{\'c} and Savin
(2000) for Siegel Levi subgroups of the groups $SO_{4n}$ and $Sp_{4n}$ under
the local Jacquet-Langlands correspondence. It can be applied to a simply
connected simple $F$-group of type $E_6$ or $E_7$, and a connected reductive
$F$-group of type $A_{n}$, $B_{n}$, $C_n$ or $D_n$.
