Let $G$ be a graph. For a subset $X$ of $V(G)$, the switching $σ$ of $G$ is the signed graph $G^σ$ obtained from $G$ by reversing the signs of all edges between $X$ and $V(G)\setminus X$. Let $A(G^σ)$ be the adjacency matrix of $G^σ$. An eigenvalue of $A(G^σ)$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let $S_{n,k}$ be the graph obtained from the complete graph $K_{n-r}$ by attaching $r$ pendent edges at some vertex of $K_{n-r}$. In this paper we prove that there exists a switching $σ$ such that all eigenvalues of $G^σ$ are main when $G$ is a complete multipartite graph, or $G$ is a harmonic tree, or $G$ is $S_{n,k}$. These results partly confirm a conjecture of Akbari et al.