In the temperature-concentration phase diagram of most iron-based superconductors, antiferromagnetic order is gradually suppressed to zero at a critical point, and a dome of superconductivity forms around that point. The nature of the magnetic phase and its fluctuations is of fundamental importance for elucidating the pairing mechanism. In Ba1-xKxFe2As2 and Ba1-xNaxFe2As2, it has recently become clear that the usual stripelike magnetic phase, of orthorhombic symmetry, gives way to a second magnetic phase, of tetragonal symmetry, near the critical point, in the range from x=0.24 to x=0.28 for Ba1-xKxFe2As2. In a prior study, an unidentified phase was discovered for x<0.24 but under applied pressure, whose onset was detected as a sharp anomaly in the resistivity. Here we report measurements of the electrical resistivity of Ba1-xKxFe2As2 under applied hydrostatic pressures up to 2.75 GPa, for x=0.22, 0.24, and 0.28. The critical pressure above which the unidentified phase appears is seen to decrease with increasing x and vanish at x=0.24, thereby linking the pressure-induced phase to the tetragonal magnetic phase observed at ambient pressure. In the temperature-concentration phase diagram of Ba1-xKxFe2As2, we find that pressure greatly expands the tetragonal magnetic phase, while the stripelike phase shrinks. This reveals that pressure may be a powerful tuning parameter with which to explore the interplay between magnetism and superconductivity in this material.