We present a modified velocity map imaging (VMI) spectrometer to be used in angle-resolved molecular photoionization studies in the gas phase with synchrotron radiation (SR) in the VUV/soft x-ray range. The main modifications as compared to the original design of Eppink and Parker [A. T. J. B. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997)] are an open repeller which allows the VMI spectrometer to be coupled to an independent dispersive electrostatic analyzer for combined operation in coincidence mode experiments, and the introduction of a coupled double Einzel lens in the flight tube in order to collect the full 4π solid angle for higher kinetic energy particles. The length and position of the lenses have been optimized by a genetic algorithm to obtain the maximum kinetic energy possible without compromising the energy resolution. Ray-tracing simulations and SR experiments show that the lenses can increase the kinetic energy bandwidth by a factor of up to 2.5. Furthermore, a remarkable improvement in the radial focusing of the particles’ momenta can be achieved when the lens array is operated in optimum fashion. The accuracy in the determination of the angular parameters, already satisfactory in the original VMI design, is not compromised by the lens operation. Experimentally, we succeeded in collecting 4π electrons with 14eV kinetic energy and 6% relative energy resolution with a detector of 36mm effective diameter, despite the larger ionization volume given by the SR as compared to laser multiphoton experiments. We predict that, by changing to a detector diameter of 70mm and reducing the focal length by a third, particles with energies up to 200eV could be collected by applying 10kV to the repeller electrode.