Let \(H({\mathbb {B}})\) denote the space of all holomorphic functions on the unit ball \({\mathbb {B}}\) of \( {\mathbb {C}}^n\), \(\psi _1,\psi _2,\psi _3\in H({\mathbb {B}}) \) and \(\varphi \) be a holomorphic self-map of \( {\mathbb {B}}\). This paper studies the boundedness and compactness of the following extension of the Stevic–Sharma operator, recently proposed by Liu and Yu $$\begin{aligned} T_{\psi _1, \psi _2, \psi _3,\varphi }f(z)=\psi _1(z)f(\varphi (z))+\psi _2(z){{\mathcal {R}}}f(\varphi (z))+\psi _3(z){{\mathcal {R}}}\left( f\circ \varphi \right) (z), z\in {\mathbb {B}}, \end{aligned}$$ where \({{\mathcal {R}}}f(z)\) is the radial derivative of \(f\) at \(z\), from the general space \(F(p, q, s)\) to the weighted-type space \(H_{\mu }^\infty \) or the little weighted-type space \(H_{\mu ,0}^\infty \) on the unit ball.