Let $G$ be a simple graph without isolated vertices with edge set $E(G)$, and let $j$ and $k$ be two positive integers. A function $f\:E(G)\rightarrow \{-1, 1\}$ is said to be a signed star $j$-dominating function on $G$ if $\sum_{e\in E(v)}f(e)\ge j$ for every vertex $v$ of $G$, where $E(v)=\{uv\in E(G)\mid u\in N(v)\}$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct signed star $j$-dominating functions on $G$ with the property that $\sum_{i=1}^df_i(e)\le k$ for each $e\in E(G)$, is called a signed star $(j,k)$-dominating family (of functions) on $G$. The maximum number of functions in a signed star $(j,k)$-dominating family on $G$ is the signed star $(j,k)$-domatic number of $G$ denoted by $d^{(j,k)}_{SS}(G)$.In this paper we study properties of the signed star $(j,k)$-domatic number of a graph $G$. In particular, we determine bounds on $d_{SS}^{(j,k)}(G)$. Some of our results extend those ones given by Atapour, Sheikholeslami, Ghameslou and Volkmann [1] for the signed star domatic number, Sheikholeslami and Volkmann [5] for the signed star $(k,k)$-domatic number and Sheikholeslami and Volkmann [4] for the signed star $k$-domatic number.