Freeform lenses can be designed for diverse illumination profiles with good uniformity. However, most of the previous studies were formulated for a single point source and the lens were designed to have a spherical bottom. In this study, the formulation is extended for multiple point sources and for lenses with a flat bottom in favor of prototyping and manufacturing. The extended formulation requires only a freeform surface to design. However, it could be over determined if the light rays emitted from the multiple point sources overlap at the near field. The weighted least-square method is introduced to solve the over-determined problem. A weighting function correlated with the emitting intensities of the sources is proposed to design for illumination profile fit and uniformity in trade-off. The adequacy of the extended formulation is demonstrated by simulation. Circular and rectangular illuminations of multiple point sources in different layouts are illustrated. The simulation results show that profile fit and uniformity could be significantly affected by a source offset. With the offset taken into account in the extended formulation, the effects can be properly collimated.