Maybe I can expand Fullwings as I think we work for the same.
An FO can call STOP but only for the events which a Captain is also obliged to also call STOP. Although fleet specific, they are typically (but not wholely universally) say:
Airbus
Fire
Engine failure with 2+ parameters at least one internal
ECAM Red Warning
Boeing
Fire
Failure (as above)
Config Warning
Windshear Ahead
Monitor Radar Display
These are events that the Captain MUST call STOP for so the take-off HAS to be rejected. It is only in these circumstances that the FO can call STOP. The discretion to call STOP in any other circumstances remains with the Captain and the FO(s) is/are to bring the failure to his/her attention.
We don't have the full discretion over the decision to reject as I think was being implied by some here (not you FW).