In this paper we present a new method which allows verification of whether a given planar parallel RPR manipulator can be extended to become an overconstrained mechanism, which has the same solutions for the forward kinematics (FK) problem as the original manipulator. In most cases it is possible to design such an overconstrained manipulator. With this method it is very easy to calculate the coordinates of the fourth base and platform points and the length of the fourth leg. It follows that the coordinatesof possible attachment points depend only on the geometry of the base and platform but not the lengths of the three legs. The procedure (algorithm) we discuss herein employs the kinematic mapping of planar displacements. A numerical example is given to illustrate the algorithm.