Flexible power point tracking (FPPT) is the control of active power generated by grid-connected photovoltaic power plants (GCPVPPs) to provide grid-support functionality. An FPPT algorithm for the reduction of the extracted power from photovoltaic (PV) strings during voltage sags was previously proposed by the authors. An advantage of this algorithm, compared to conventional FPPT algorithms, was its fast dynamics facilitated by use of a simple PI controller that dynamically modifies the PV voltage reference. The previously proposed scheme could only be employed for the short-duration in which the power system experiences a voltage sag. A novel modification to this algorithm with multi-mode operation is introduced in this letter, which provides FPPT capability for continuous operation of GCPVPPs. Unlike the previous algorithm, which was able to only move the operation point to the right-side of MPP, the proposed algorithm in this letter is able to move the operation point to both right- and left-sides of the MPP that provides the flexibility to operate in the optimum operation region for both single- and two-stage GCPVPPs. Experimental results are provided to demonstrate the performance of the proposed algorithm under dynamic irradiance conditions.