The TwinMic spectromicroscope at Elettra is a multipurpose experimental station for full-field and scanning imaging modes and simultaneous acquisition of X-ray fluorescence. The actual LEXRF detection setup consists of eight single-cell Silicon Drift Detectors (SDD) in an annular configuration. Although they provide good performances in terms of both energy resolution and low-energy photon detection efficiency, they cover just about 4% of the whole photoemission solid angle. This is the main limitation of the present detection system, since large part of the emitted photons is lost and consequently a high acquisition time is required. In order to increase the solid angle, a new LEXRF detection system is being developed within a large collaboration of several institutes. The system, composed of 4 trapezoidal multi-cell silicon drift detectors, covers up to 40% of the photoemission hemisphere, so that this geometry provides a 10 times improvement over the present configuration. First measurements in the laboratory and on the TwinMic beamline have been performed in order to characterize a single trapezoidal detector, configured and controlled by means of two multichannel ASICs, which provide preamplification, shaping and peak-stretching, connected to acquisition electronics based on fast ADCs and FPGA and working under vacuum.