  Let $\mathcal{M}_i$ be a family of $\mathrm{II}_1$-factors, containing a
common $\mathrm{II}_1$-subfactor $\mathcal{N}$, such that
$[\mathcal{M}_i:\mathcal{N}] \in \mathbb{N}_0$ for all $i$. Furthermore, let
$\phi \colon \mathbb{N}_0 \to \mathbb{C}$. We show that if a Hankel matrix
related to $\phi$ is trace-class, then there exists a unique completely bounded
map $M_\phi$ on the amalgamated free product of the $\mathcal{M}_i$ with
amalgamation over $\mathcal{N}$, which acts as an radial multiplier. Hereby we
extend a result of U. Haagerup and the author for radial multipliers on reduced
free products of unital $C^*$- and von Neumann algebras.
