This paper introduces a new phase-variable switch control for the parallel synchronized triple bias-flip (P-S3BF) interface circuit, towards the broadband and high-capability piezoelectric energy harvesting (PEH) systems. By using the phase-variable P-S3BF (PV-P-S3BF), both the electrically induced damping and electrically induced mass/stiffness can be tuned to a certain extent in operation, such that to simultaneously make the dual tasks of broadband and high-capability in PEH. The joint dynamics and harvested power of the PEH systems using the PV-P-S3BF circuits are thoroughly discussed based on the harmonic analysis and impedance modeling. The available range of PV-P-S3BF is rationally shown in the complex impedance plane. The experimental results obtained with a PCB-level prototyped circuit show agreement with the analytical results. The new PV-P-S3BF circuit opens a promising future towards the electrically in-situ tunable broadband and high-capability PEH systems.