It is a quite commonly encountered case that the mathematical modelling of a system involves more than one functions. If these functions are especially multivariate then the computational complexity to deal with these functions becomes higher. This urges us to use Vector High Dimensional Model Representation (VHDMR) where a vector valued multivariate function is expressed in terms of some other vector valued functions in ascending multivariance. The components of this additive representation are determined in such a way that the integral of any nonconstant vector component's integral with respect to its one of independent variables over a prescribed interval after multiplying by an appropriate matrix weight vanishes. Despite the whole VHDMR contains a finite number of additive terms only the truncations at few leading terms are preferred to be used to approximate the function being target of VHDMR. In this work a new approach (we call Piecewise VHDMR) is developed to get higher approximation qualities. Piecewise VHDMR is based on an optimised domain splitting, which may differ from element to element of the vector valued function under consideration, to get maximum constancy for VHDMR.