Multiple superconducting order parameters are extremely rare. Here we show that a very small pressure can induce this phenomenon in the recently discovered heavy fermion superconductor UTe2. This nearly ferromagnetic system shows several intriguing phenomena, including an extraordinary reinforcement of superconductivity in very strong magnetic fields. We find that pressure can tune the system to a more correlated state and probable magnetic order. The superconducting critical temperature is strongly enhanced, reaching almost 3K, a new record for Ce-and U-based heavy fermion superconductors. Most spectacularly under pressure we find a transition within the superconducting state, putting UTe2 among the very rare systems having multiple superconducting phases. UTe2 under pressure is a treasure trove of several of the most fascinating phenomena in unconventional superconductivity and may well be a keystone in their understanding.In most superconductors the superconducting order parameter is s-wave, meaning it has the same symmetry as the crystal lattice. However in the ever expanding family of unconventional superconductors, which includes such disparate members as high-Tc cuprates and pnictides, organic superconductors, and heavy fermions, the order parameter can assume a number of different symmetries, usually lower than the lattice symmetry. This opens the intriguing possibility that a given system could in principle exhibit different order parameters, each one being selected by changing an external variable like temperature or magnetic field. This scenario does in fact exist, but is extremely rare, having been really established only in superfluid 3 He[1] and in two superconductors: UPt3[2,3] and thorium-doped UBe13 [4]. The recently discovered superconductivity in the heavy fermion system UTe2 [5] shows several unusual properties, the most spectacular being re-entrant superconductivity when magnetic fields as high as 60 Tesla are applied in specific directions [6][7][8][9]. Another intriguing property is the temperature dependence of the specific heat. Indeed in all samples a large residual term, of about 50% of the normal state specific heat, seems to remain as the temperature approaches zero [5,6].In this report we show that the superconductivity is extremely sensitive to hydrostatic pressure as a tuning parameter and that UTe2 is probably another example of multiple superconducting phases. The superconducting state found at zero pressure is monotonously depressed with pressure but a second superconducting state is found to emerge as pressure is increased. Pressure increases the splitting between the 2 transitions and the high temperature superconducting transition reaches nearly 3K, a new record for a U-based heavy fermion superconductor. Pressure also drives the system towards a more correlated state, with evidence for a strong enhancement of the electronic effective mass. At a critical pressure of about 1.7 GPa both superconducting states are suppressed and a new order parameter, probably magnetic, is foun...