The heavy fermion compound Ce3Pd20Si6 displays unconventional quantum criticality as the lower of two consecutive phase transitions is fully suppressed by magnetic field. Here we report on the effects of pressure as an additional tuning parameter. Specific heat and electrical resistivity measurements reveal a converse effect of pressure on the two transitions, leading to the merging of both transitions at 6.2 kbars. The field-induced quantum criticality is robust under pressure tuning. We rationalize our findings within an extended version of the global phase diagram for antiferromagnetic heavy fermion quantum criticality.