Poly(N-isopropylacrylamide) (PNIPAM) in aqueous solution forms mesoglobules above its cloud point temperature Tcp. While these are small and compact at atmospheric pressure, they are large and water-rich at high pressure. To identify the transition between these states, we employed optical microscopy and carried out isothermal pressure scans. Using very small angle neutron scattering, we determined the size and water content of the mesoglobules in pressure scans at different temperatures above Tcp. We observe a distinct transition at pressures of 35-55 MPa with the transition pressure depending on temperature. While the transition is smooth at high temperatures, i.e., far away from the coexistence line, it is abrupt at low temperatures, i.e., close to the coexistence line. Hence, at high temperatures, the swelling of the mesoglobules dominates, whereas at low temperatures, the coalescence of mesoglobules prevails. Subsequently decreasing the pressure results in a gradual deswelling of the mesoglobules at high temperature. In contrast, at low temperatures, small and compact mesoglobules form, but the large aggregates persist. We conclude that, on the time scale of the experiment, the disintegration of the large swollen aggregates into small and compact mesoglobules is only partially possible. Erasing the history by cooling the sample at the maximum pressure into the one-phase state does not result in qualitative changes for the behavior with the only difference that Fewer mesoglobules are formed when the pressure is decreased again. The newly identified transition line separates the low-pressure from the high-pressure regime.