  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.
