TORoidal Plasma EXperiment (TORPEX) is a Simple Magnetized Torus featuring open helical magnetic field lines obtained from the superposition of a small vertical component on the main toroidal field. This work introduces the experimental setup developed to include a poloidal magnetic field. The toroidal and poloidal fields generate a rotational transform, making the magnetic geometry of TORPEX closer to that of a tokamak. This upgrade opens the possibility to deal with closed and open flux surfaces, as well as with the transition region across the last closed flux surface. The main technical solutions are discussed together with the physical considerations at the basis of the system design. Selected examples of the magnetic configurations accessible with the set of magnetic field coils available on TORPEX are discussed, ranging from single-null X-points to magnetic snowflakes. The simplest magnetic configuration of quasi-circular concentric flux surfaces is tested experimentally. Measurements of the two-dimensional electron plasma density profiles and the particle confinement time are presented, together with the first steps towards the understanding of plasma production mechanisms. (C) 2014 AIP Publishing LLC.