Let $L(\mathbb F_2)$ be the group von Neumann algebra of the free group on two generators. The interpolated free group factors of Dykema and Radulescu are defined as $L(\mathbb F_r)=L(\mathbb F_2)^{1/\sqrt{r-1}}$ for $r>1$, where $M^s$ denotes the amplification of the $\mathrm{II}_1$ factor $M$. This notation is consistent with the usual free group factors in the sense that if $r$ is an integer, then $L(\mathbb F_r)$ is isomorphic to the group von Neumann algebra of $\mathbb F_r$.
If $A=L(\mathbb F_r)$ and $B$ is a finite-dimensional von Neumann algebra with dimension $l$, living in a bigger tracial von Neumann algebra such that $A$ and $B$ are $\ast$-free, is there any formula to calculate the free product $L(\mathbb F_r)\ast B$?