  The heavy fermion material UTe$_2$ possesses a rich phase diagram with
multiple superconducting phases, several of which exhibit characteristics of
odd-parity pairing. Here, we report on the pressure dependence of signatures of
the superconducting transition in the temperature dependent ac magnetic
susceptibility $\chi(T)$ in high quality UTe$_2$ single crystals. We resolve a
single superconducting transition in $\chi(T)$ at low pressures $<$ 0.3 GPa. At
higher pressure, however, a second feature emerges in $\chi(T)$, which is
located at the thermodynamic phase boundary between two separate
superconducting states previously identified by specific heat studies. The
observation of a two-step transition in $\chi(T)$ can be understood as a
consequence of the change in the London penetration depth, when UTe$_2$
switches from one superconducting phase into another.
