Here, generalizing the class $(\Lambda^1,\Lambda^2)^*BV^{(p)}([0,2\pi]^2)$ to the class $(\Lambda^1,\Lambda^2)^*BV^{(p,q)}([0,2\pi]^2)$ of functions of $p,q$-$(\Lambda^1,\Lambda^2)^*$-bounded variation, it is observed that the class is a Banach space with respect to the pointwise operations and the generalized variation norm. Moreover, we estimate the order of magnitude of multiple Fourier coefficients of a function of this class.