In this paper, we establish the Hyers–Ulam–Rassias stability of the system of functional equations $$\begin{cases} f(x_1, x_2, \dots, x_{i_r−1}, a + b, x_{i_r+1}, \dots, x_n) = f(x_1, x_2, \dots, x_{i_r−1}, a, x_{i_r+1}, \dots, x_n) \\ +f(x_1, x_2, \dots, x_{i_r−1}, b, x_{i_r+1}, \dots, x_n), \\ f(x_1, x_2, \dots, x_{j_s−1}, a + b, x_{j_s+1}, \dots, x_n) + f(x_1, x_2, \dots, x_{j_s−1}, a − b, x_{j_s+1}, \dots, x_n)\\ = 2f(x_1, x_2, \dots, x_{j_s−1}, a, x_{j_s+1}, \dots, xn) + 2f(x_1, x_2, \dots, x_{j_s−1}, b, x_{j_s+1}, \dots, x_n)\end{cases}$$ in Fréchet spaces, where $1 \leq i_1 < i_2 < \dots < i_k < n,$ $1 < j_1 < j_2 < \dots < j_{n−k},$ ${1, 2, \dots, n} = \{i_1, i_2, \dots, i_k\} \cup \{j_1, j_2, \dots, j_{n−k}\}$.