You need to have your Z_PROBE_OFFSET_FROM_EXTRUDER set accurately. And... It may help to turn off the software endstops:
#define min_software_endstops true // If true, axis won't move to coordinates less than HOME_POS.
#define max_software_endstops true // If true, axis won't move to coordinates greater than the defined lengths below.
It sounds like you are using Grid leveling. In all of the Mesh leveling schemes (including UBL at [github.com]), going below 0.000mm is assumed to be necessary.
If you bring up the UBL system, I'll spend the time to help get over any problems you run into.
#define min_software_endstops true // If true, axis won't move to coordinates less than HOME_POS.
#define max_software_endstops true // If true, axis won't move to coordinates greater than the defined lengths below.
It sounds like you are using Grid leveling. In all of the Mesh leveling schemes (including UBL at [github.com]), going below 0.000mm is assumed to be necessary.
If you bring up the UBL system, I'll spend the time to help get over any problems you run into.