The ALICE Muon Trigger is currently yielded by a detector currently composed of 72 Bakelite single-gap Resistive Plate Chambers operated in maxi-avalanche mode, arranged in four 5.5x6.5 m2 detection planes. In order to meet the requirements posed by the forthcoming LHC high luminosity runs starting from 2021 onwards, in which ALICE will be read out in continuous mode, the Muon Trigger will become a Muon Identifier and will undergo a major upgrade. In the current setup, signals from about 21k strips are discriminated by 2400 non-amplified Front End (FEE) cards, whose thresholds are provided by external analog voltages (one for each chamber side). All these cards will be replaced with discriminators equipped with a pre-amplification stage which will allow a reduction in the operating high voltage of the detectors, thus prolonging their lifetime. Furthermore, their reference thresholds will be passed via wireless (and I2C chained per chamber side) allowing the tuning of the values at the single card level. Moreover, the 24 most exposed chambers will be replaced with new ones, equipped with high-quality (i.e. smoother surface) Bakelite laminates. The tests performed on the new FEE cards, used both in a test bench and on detectors, and on the new RPC chambers (with cosmic rays) are reported.